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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418426HAP_GCOMPLEX_SETUP:=[true];
HAP_GCOMPLEX_LIST:=
[ [ rec(
TheMatrixStab :=
Group([ [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, -1, 0, 0,
-1, 0, -1, -2 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ -2, -1, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 0, -1, 0, 0,
-1, 0, -1, -2 ], [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ -2, -1, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 1 ],
ListSign := [ 1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ] ) ), rec(
TheMatrixStab :=
Group([ [ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 0, -1,
0, -4, -1, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 1, 0, 0, 2, 0, 2, 0, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ -2, -3, -3, -1, -4, -5, -2, -4, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 2, 2, 2, 1, 0 ],
[ 1, 2, 1, 0, 4, 2, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 2, 1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 0, 0, -1, -1, -4, -3, -2 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 2, 1, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
[ -2, -1, -2, -1, 0, -1, -1, -2, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, 0, 0, -2, -2, -2 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -4, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, -1, 0, 0, 0, 0 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ 0, -1, -2, -1, -4, -6, -3, -8, -4, -2 ],
[ -2, -2, -1, -1, 0, 2, 0, 4, 1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 1, 2, 1, 0, -1, 0, -4, -1, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 0, -1,
0, -4, -1, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 2, 1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 0, 0, -1, -1, -4, -3, -2 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 2, 1, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
[ -2, -1, -2, -1, 0, -1, -1, -2, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, 0, 0, -2, -2, -2 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -4, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, -1, 0, 0, 0, 0 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ 0, -1, -2, -1, -4, -6, -3, -8, -4, -2 ],
[ -2, -2, -1, -1, 0, 2, 0, 4, 1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 1, 2, 1, 0, -1, 0, -4, -1, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 1 ],
ListSign := [ 1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ] ) ) ], [ rec(
TheMatrixStab :=
Group([ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ -2, -1, 0, 0, 0, 0,
0, 0, 0, 0 ], [ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, -2, 0,
0, 0, 0, 0 ], [ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -2, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 1, 2 ],
ListSign := [ 1, -1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 1, 0, 0, 2, 0, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, -2, 0, -4, -1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -3, -4, -2, -4, -6, -3, -8, -4, -2 ],
[ 0, 2, 2, 1, 4, 6, 3, 8, 4, 2 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ 0, -2, -2, -1, -8, -8, -4, -8, -4, -2 ],
[ 0, 0, 0, 0, 4, 4, 2, 4, 2, 1 ] ] ] ) ), rec(
TheMatrixStab :=
Group([ [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 0, 0, 1, 0, 0, 1, 0,
2, 1, 0 ], [ 0, 1, 0, 0, 2, 1, 1, 0, 0, 0 ],
[ 0, -2, -2, -1, -4, -4, -3, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, -2, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -4, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 4, 4, 2, 4, 2, 1 ] ],
[ [ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 1, 1, 0, 2, 3, 1, 4, 1, 0 ],
[ -2, -3, -3, -1, -4, -5, -2, -4, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 0, 1, 0, 0, 2, 0, 2, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, -4, -3, 0, -2, 0, 0 ],
[ 1, 2, 1, 0, 4, 2, 0, 1, 0, 0 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 2, 2, 1, 4, 2, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 0, 0, 0, 0, 2, 0, 4, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -4, -4, -1, -4, -1, 0 ],
[ 0, 0, 0, 0, 4, 4, 2, 4, 2, 1 ] ],
[ [ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -3, -5, -3, -4, -7, -4, -12, -7, -4 ],
[ -2, -1, -1, 0, 0, 1, 1, 4, 3, 2 ],
[ 4, 4, 5, 2, 4, 5, 2, 4, 1, 0 ],
[ 1, 2, 3, 2, 4, 6, 4, 9, 6, 4 ],
[ 2, 2, 2, 1, 0, -2, -2, -6, -5, -4 ],
[ -4, -6, -7, -4, -8, -8, -4, -6, -2, 0 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ],
[ -4, -2, 1, 2, 0, 2, 2, 2, 1, 0 ],
[ 4, 4, 2, 0, 4, 2, 0, 1, 0, 0 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ], [ 0, 0, 0, 0, 0, 1, 1,
0, 0, 0 ], [ 0, 0, 0, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, -1, -1, 0, -2, -2, -6, -4, -2 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -4, -3, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -2, 0, -6, -1, 0 ],
[ 1, 2, 3, 1, 4, 6, 2, 9, 3, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 1, 1, 0, 0, 1, 0, 2, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, -2, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 2, 1, 0 ],
[ 0, 1, 1, 1, 0, -1, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 1, 1, 0, 0, -1, 0, -2, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 2, 2 ],
ListSign := [ 1, -1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -3, -5, -3, -4, -7, -4, -12, -7, -4 ],
[ -2, -1, -1, 0, 0, 1, 1, 4, 3, 2 ],
[ 4, 4, 5, 2, 4, 5, 2, 4, 1, 0 ],
[ 1, 2, 3, 2, 4, 6, 4, 9, 6, 4 ],
[ 2, 2, 2, 1, 0, -2, -2, -6, -5, -4 ],
[ -4, -6, -7, -4, -8, -8, -4, -6, -2, 0 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ],
[ -4, -2, 1, 2, 0, 2, 2, 2, 1, 0 ],
[ 4, 4, 2, 0, 4, 2, 0, 1, 0, 0 ] ] ] ) ) ], [ rec(
TheMatrixStab :=
Group([ [ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, -2, 0,
0, 0, 0, 0 ], [ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, -1, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, -1, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, -2, 0,
0, 0, 0, 0 ], [ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 1, 1, 2 ],
ListSign := [ 1, -1, 1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, -1, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 1, 0, 0, 2, 0, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, -2, 0, -4, -1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -3, -4, -2, -4, -6, -3, -8, -4, -2 ],
[ 0, 2, 2, 1, 4, 6, 3, 8, 4, 2 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ 0, -2, -2, -1, -8, -8, -4, -8, -4, -2 ],
[ 0, 0, 0, 0, 4, 4, 2, 4, 2, 1 ] ] ] ) ), rec(
TheMatrixStab :=
Group([ [ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, -1, -1, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -1, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, -2, 0,
0, 0, 0, 0 ], [ 0, 1, 1, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, -1, -2, -1, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 1, 1, 1, 1 ],
ListSign := [ 1, -1, -1, 1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, -1, -1, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -1, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, -1, -2, -1, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ] ] ) ) ], [ rec(
TheMatrixStab :=
Group([ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ -2, -1, 0, 0, 0, 0,
0, 0, 0, 0 ], [ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -2, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -2, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 2, 1, 0, 0, 0,
0, 0, 0 ], [ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -2, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 1, 1, 1, 1, 2 ],
ListSign := [ 1, -1, -1, 1, 1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -2, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ] ] ) ), rec(
TheMatrixStab :=
Group([ [ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ], [ 0, 0, 0, -1, 0, 0,
-1, 0, -1, -2 ], [ 0, 0, -1, 0, 0, -1, 0, -2, -1, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, -2, -1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ -2, -1, -1, -1, 0, 1, 0, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, -1, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, -1, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, -1, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, -2, -1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ -2, -1, -1, -1, 0, 1, 0, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 1, 1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 2, 0, 0 ],
[ 0, -1, -1, 0, -2, -3, -1, -4, -1, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, 0, 0 ],
[ -2, -1, -1, -1, 0, 1, 0, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, -1, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, -2, -1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ -2, -1, -1, -1, 0, 1, 0, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, -2, -1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ -2, -1, -1, -1, 0, 1, 0, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, -2, -1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ -2, -1, -1, -1, 0, 1, 0, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ], [ 0, 1, 1, 0, 0, -1,
0, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 2, 0, 0 ],
[ 0, -1, -1, 0, -2, -3, -1, -4, -1, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, 0, 0 ],
[ -2, -1, -1, -1, 0, 1, 0, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 1, 1, 1, 1, 2, 2, 2, 2 ],
ListSign := [ 1, -1, -1, 1, 1, -1, -1, 1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, -2, -1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ -2, -1, -1, -1, 0, 1, 0, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 0, -1, -1, 0, 0, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, -1, -1, 0, -2, -3, -1, -4, -1, 0 ],
[ 0, 1, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 1, 1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 0, -1, -1, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 ],
[ -2, -2, -2, -1, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ -2, -2, -2, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 2, 1, 0 ],
[ 2, 1, 0, 1, 0, -1, 0, -2, -1, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ -2, -1, 0, 0, 0, 1, 0, 2, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ] ] ) ), rec(
TheMatrixStab :=
Group([ [ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -1,
0, -2, 0, 0 ], [ 0, -1, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 2, 2, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, -1, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -2, -1, -1, -2, -1, -1, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 0, 2, 1, 0, 2, 1, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 4, 2, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 2, 1, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -2, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, -1,
0, -2, 0, 0 ], [ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, 0, 1, 1, 2, 1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 1, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -2, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 2, 2, 0, -1, 2, 0, -1, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -2, -1, 1, -2, -1, 1, 0, 1, 0 ],
[ 1, 1, 0, -1, 1, 0, -1, 0, 0, 1 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ],
ListSign := [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, -1, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 2, 2, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, -1, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -2, -1, -1, -2, -1, -1, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 0, 2, 1, 0, 2, 1, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 4, 2, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 2, 1, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 2, 2, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 4, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -2, -3, -1, -2, -3, -1, -4, -1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 2, 0, -1, -2, -1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -2, 1, 1, -2, 1, 1, 0, 0, 0 ],
[ 1, 1, -1, -1, 1, -1, -1, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, 0, 1, 1, 2, 1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, -2, -2, 0, -2, 0, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, -1, 1, 1, -2, 0, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 2, 0, -1, -2, -1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, -1, -1, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 1, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -2, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 2, 2, 0, -1, 2, 0, -1, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -2, -1, 1, -2, -1, 1, 0, 1, 0 ],
[ 1, 1, 0, -1, 1, 0, -1, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, 0, -1, -1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -2, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, -1, 0, 1, -2, 0, 1, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, -2, -2, 0, -2, 0, 0 ],
[ 0, 1, 0, -1, 2, 1, -1, 0, -1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, -1, 0, 0, 1 ] ] ] ) ), rec(
TheMatrixStab :=
Group([ [ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, -2, 0,
0, 0, 0, 0 ], [ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, -1, -2, -1, 0 ],
[ 0, 1, 1, 0, 2, 2, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 1, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -2, -2, -2 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, -1, -2, -1, 0 ],
[ 0, 1, 1, 0, 2, 2, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 1, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -2, -2, -2 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0,
0, 0, 0 ], [ 0, 0, 0, 0, 0, -1, 0, -2, -1, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, -1, 0, 0, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 1, 1, 1, 0, -1, -1, -2, -2, -2 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, -2, -2, -2 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 2, 2, 2, 2, 2, 2 ],
ListSign := [ 1, -1, 1, -1, 1, -1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, -1, -2, -1, 0 ],
[ 0, 1, 1, 0, 2, 2, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 1, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -2, -2, -2 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 2, 1, 0 ],
[ 0, 1, 1, 1, 0, -1, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 1, 1, 0, 0, -1, 0, -2, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 2, 2, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -3, -2, -4, -3, -2 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ] ] ) ) ], [ rec(
TheMatrixStab :=
Group([ [ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ], [ 0, 0, 0, 1, 0, 0, 1,
0, 1, 0 ], [ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 1, 2, 1, 2, 3, 1, 4, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 1, 2, 1, 2, 3, 1, 4, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 1, 2, 1, 2, 3, 1, 4, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 1, 2, 1, 2, 3, 1, 4, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 1, 2, 1, 2, 3, 1, 4, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -3, -2, -4, -3, -2 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 0, 0, -1, 0, 0,
0, 0, 0, 0 ], [ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -3, -2, -4, -3, -2 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -2, -1, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 1, 1, 1, 1, 1, 1, 2, 2, 2 ],
ListSign := [ 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 1, 2, 1, 2, 3, 1, 4, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -3, -2, -4, -3, -2 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, -1, -4, -3, -2 ],
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[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -2, -1, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
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[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -2, -2, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 1, 1, 2, 2, 1, 2, 1, 0 ],
[ 0, -1, -2, -1, -2, -3, -1, -4, -1, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, -1, -1, -1, -2, -2, -2, -2, -2, -2 ],
[ 0, 1, 2, 1, 2, 3, 2, 4, 3, 2 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -3, -2, -4, -3, -2 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, -1, -2, -1, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ] ) ), rec(
TheMatrixStab :=
Group([ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 2, 1, 0, 0, 0,
0, 0, 0 ], [ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -2, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
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[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 2, 2, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -2, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -3, -1, 0, -4, -1, 0, 0, 0, 0 ],
[ 2, 3, 2, 1, 4, 2, 1, 0, 0, 0 ],
[ 1, 2, 1, 0, 4, 2, 0, 1, 0, 0 ],
[ -2, -4, -3, -1, -8, -6, -2, -4, -1, 0 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
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[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ -2, -2, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, -1, 0, 0, 1 ],
[ 0, -1, 0, 1, -4, -1, 2, 0, 1, 0 ],
[ 0, 1, 0, -1, 4, 2, -1, 0, -2, -2 ],
[ 1, 2, 1, 0, 4, 2, 0, 1, 0, 0 ],
[ -2, -4, -3, -1, -8, -6, -2, -4, -1, 0 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 2, 0, 0, 0, 0, 0, 0 ],
[ -2, -2, -3, -2, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 2, 4, 4, 4 ],
[ 0, -1, -2, -2, -4, -7, -6, -12, -10, -8 ],
[ 0, 1, 2, 2, 4, 6, 5, 8, 6, 4 ],
[ 1, 2, 3, 2, 4, 6, 4, 9, 6, 4 ],
[ -2, -4, -5, -3, -8, -10, -6, -12, -7, -4 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
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[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -2, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
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[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -2, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -3, -1, 0, -4, -1, 0, 0, 0, 0 ],
[ 2, 3, 2, 1, 4, 2, 1, 0, 0, 0 ],
[ 1, 2, 1, 0, 4, 2, 0, 1, 0, 0 ],
[ -2, -4, -3, -1, -8, -6, -2, -4, -1, 0 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 2, 0, 0, 0, 0, 0, 0 ],
[ -2, -2, -3, -2, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 2, 4, 4, 4 ],
[ 0, -1, -2, -2, -4, -7, -6, -12, -10, -8 ],
[ 0, 1, 2, 2, 4, 6, 5, 8, 6, 4 ],
[ 1, 2, 3, 2, 4, 6, 4, 9, 6, 4 ],
[ -2, -4, -5, -3, -8, -10, -6, -12, -7, -4 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 2, 2, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -2, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -3, -1, 0, -4, -1, 0, 0, 0, 0 ],
[ 2, 3, 2, 1, 4, 2, 1, 0, 0, 0 ],
[ 1, 2, 1, 0, 4, 2, 0, 1, 0, 0 ],
[ -2, -4, -3, -1, -8, -6, -2, -4, -1, 0 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -2, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ -2, -1, -2, -2, 0,
0, 0, 0, 0, 0 ], [ 0, 0, 1, 2, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 2, 1, 2, 2, 4, 4, 4 ],
[ 0, 0, -1, -2, 0, -1, -2, -4, -6, -8 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 2, 4 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 2, 4 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -4 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, -2, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, -1, 1, 0, -1, 0, 0, 1 ],
[ 0, 0, 1, 2, 0, 1, 2, 0, -1, -4 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 2, 4 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -4 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4 ],
ListSign := [ 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1,
1, 1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -2, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -3, -1, 0, -4, -1, 0, 0, 0, 0 ],
[ 2, 3, 2, 1, 4, 2, 1, 0, 0, 0 ],
[ 1, 2, 1, 0, 4, 2, 0, 1, 0, 0 ],
[ -2, -4, -3, -1, -8, -6, -2, -4, -1, 0 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 2, 0, 0, 0, 0, 0, 0 ],
[ -2, -2, -3, -2, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 2, 4, 4, 4 ],
[ 0, -1, -2, -2, -4, -7, -6, -12, -10, -8 ],
[ 0, 1, 2, 2, 4, 6, 5, 8, 6, 4 ],
[ 1, 2, 3, 2, 4, 6, 4, 9, 6, 4 ],
[ -2, -4, -5, -3, -8, -10, -6, -12, -7, -4 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, -2, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, -1, 1, 0, -1, 0, 0, 1 ],
[ 0, 0, 1, 2, 0, 1, 2, 0, -1, -4 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 2, 4 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -4 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, -2 ],
[ 0, -1, -1, 0, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 2, 1, 2, 3, 2, 4, 3, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -2, -2 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -3, -3, -1, -4, -4, -1, -4, -1, 0 ],
[ 2, 2, 2, 1, 2, 2, 1, 2, 1, 0 ],
[ -2, -2, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ -2, -3, -3, -2, -4, -4, -3, -4, -3, -2 ],
[ 2, 3, 2, 1, 4, 2, 1, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ -2, -2, -1, -1, -2, -1, -1, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, -1, -1, -1, -4, -4, -3, -4, -3, -2 ],
[ 0, 0, 0, 0, 2, 2, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 1, 2 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ 0, -1, -1, 0, -4, -4, -1, -4, -1, 0 ],
[ 0, 1, 0, -1, 4, 2, -1, 0, -2, -2 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, -1, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, -4, -4, -1, -4, -1, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, -2, -3, -2, -4, -2, 0 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ 0, -1, -1, -1, -4, -4, -3, -4, -3, -2 ],
[ 0, 1, 2, 2, 4, 6, 5, 8, 6, 4 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -3, -3, -4, -4, -4 ],
[ 0, 0, 0, 0, 1, 2, 2, 4, 4, 4 ] ],
[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ -2, -3, -3, -2, -4, -4, -3, -4, -3, -2 ],
[ 2, 2, 2, 1, 2, 2, 1, 2, 1, 0 ],
[ -2, -2, -3, -2, -2, -3, -2, -4, -3, -2 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ -2, -3, -3, -1, -4, -4, -1, -4, -1, 0 ],
[ 2, 3, 4, 2, 4, 6, 3, 8, 4, 2 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -2, -3, -1, -2, -3, -1, -4, -1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 1, 1, 2, 1, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 2 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -2, -1, 1, -2, -1, 1, 0, 1, 0 ],
[ 1, 1, 0, -1, 1, 0, -1, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 1, 0 ],
[ 0, -1, -1, 0, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 1, 0, 2, 3, 2, 4, 2, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 2, 4 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ -2, -2, -3, -3, -2, -3, -3, -4, -4, -4 ],
[ 1, 1, 2, 2, 1, 2, 2, 4, 4, 4 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -3, -3, -1, -4, -4, -1, -4, -1, 0 ],
[ 2, 2, 2, 1, 2, 2, 1, 2, 1, 0 ],
[ -2, -2, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ -2, -3, -3, -2, -4, -4, -3, -4, -3, -2 ],
[ 2, 3, 2, 1, 4, 2, 1, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ -2, -2, -1, -1, -2, -1, -1, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, -1, 0, -1, -1, -2, -2, -2 ],
[ 0, 0, 1, 1, 0, 2, 2, 4, 3, 2 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ -2, -3, -3, -2, -4, -4, -3, -4, -3, -2 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, -1, -1, 0, -2, -2, -4, -3, -2 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -3, -3, -1, -4, -4, -1, -4, -1, 0 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ] ] ] ) ), rec(
TheMatrixStab :=
Group([ [ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, -2, 0,
0, 0, 0, 0 ], [ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, 0, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -2, -3, -1, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -2, -2 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 2, 2, 1, 0, 0, 0 ],
[ 0, -1, -1, -1, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, -2, -3, -2, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, -1, -2, -1, -4, -6, -3, -8, -4, -2 ],
[ 0, 1, 2, 1, 2, 3, 1, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ -2, -3, -3, -1, -4, -4, -1, -4, -1, 0 ],
[ 0, 0, 0, -1, 0, 0, -2, 0, -2, -2 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -2, -1, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -2, -2 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, -1, -2, -1, -4, -6, -3, -8, -4, -2 ],
[ 0, 1, 2, 1, 2, 3, 1, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ -2, -3, -3, -1, -4, -4, -1, -4, -1, 0 ],
[ 0, 0, 0, -1, 0, 0, -2, 0, -2, -2 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, -2, 0,
0, 0, 0, 0 ], [ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ -2, -2, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, 0, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -2, -3, -1, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -2, -2 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 1, 1, 1, 1, 1, 1, 4 ],
ListSign := [ 1, -1, 1, -1, -1, 1, 1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, 0, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -2, -3, -1, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -2, -2 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, -1, -2, -1, -4, -6, -3, -8, -4, -2 ],
[ 0, 1, 2, 1, 2, 3, 1, 4, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ -2, -3, -3, -1, -4, -4, -1, -4, -1, 0 ],
[ 0, 0, 0, -1, 0, 0, -2, 0, -2, -2 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ -2, -3, -4, -2, -4, -6, -3, -8, -4, -2 ],
[ 0, 0, 1, 0, 0, 2, 0, 4, 1, 0 ],
[ 0, 0, 0, 1, 0, 0, 2, 0, 2, 2 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -2, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, -1, -2, -3, -2, -4, -3, -2 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 2, 2 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, -1, 0 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ] ] ) ), rec(
TheMatrixStab :=
Group([ [ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ], [ 0, -1, 0, 0, -2, 0,
0, 0, 0, 0 ], [ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, -4, -4, -1, -4, -1, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 2, 1, 0 ],
[ 0, 1, 1, 0, 0, -1, -1, -2, -1, 0 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ 0, -1, -1, -1, -4, -4, -3, -4, -3, -2 ],
[ -2, -2, -1, 0, 0, 2, 2, 4, 3, 2 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 1, 1, 1, 0, -1, -1, -2, -2, -2 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 ],
[ -2, -2, -2, -1, -2, -2, -1, 0, 0, 0 ],
[ 2, 1, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 2, 1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -1, -3, -2, 0, -1, -1, -4, -3, -2 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 0, -1, -2 ],
[ 0, 0, 1, 1, 0, 0, 0, 0, 1, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 1, 0, -1, 0, 0, 1 ],
[ 0, 1, 0, -1, 0, 0, 1, 0, 0, -2 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, 0, 2 ],
[ 1, 0, 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ -2, -1, -1, -1, 0, 0, -1, 0, -1, 0 ],
[ 0, -1, 0, 1, -2, -1, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
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[ 1, 0, 0, 1, 0, 0, 0, 0, 0, 1 ],
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[ 0, 0, 0, 0, 1, 0, -1, 0, 0, 1 ] ],
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[ 0, 0, 2, 2, 0, 2, 2, 4, 3, 2 ],
[ 0, 0, -2, -2, 0, -1, -1, -2, -2, -2 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -4, -4, -6, -3, -4, -6, -3, -8, -4, -2 ],
[ 4, 3, 5, 3, 2, 3, 2, 4, 3, 2 ],
[ 4, 4, 4, 2, 4, 4, 2, 4, 2, 1 ],
[ -8, -6, -6, -4, -4, -4, -3, -4, -3, -2 ],
[ 4, 2, 2, 2, 1, 1, 1, 1, 1, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
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[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
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[ 0, 1, 1, 0, 0, 1, 1, 2, 1, 0 ],
[ 1, 0, 0, 1, 0, 0, 0, 0, 0, 1 ],
[ -4, -1, -1, -3, 0, 0, -1, 0, -1, -2 ],
[ 2, 0, 1, 2, 0, 0, 0, 0, 1, 2 ],
[ 4, 2, 2, 2, 1, 1, 1, 1, 1, 1 ],
[ -4, -1, -3, -3, 0, -1, -1, -2, -2, -2 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, -1, 0, -1, -1, 0, 0, 0 ],
[ 0, -1, 0, 1, -2, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
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[ 0, 1, 0, -1, 0, 1, 1, 0, -1, -2 ],
[ 0, 0, 0, 0, 1, 0, -1, 0, 0, 1 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ], [ 0, -1, -1, 0, -4,
-4, -1, -4, -1, 0 ], [ 0, 0, 0, 0, 2, 2, 1, 2, 1, 0 ],
[ 0, 1, 1, 0, 0, -1, -1, -2, -1, 0 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ 0, -1, -1, -1, -4, -4, -3, -4, -3, -2 ],
[ -2, -2, -1, 0, 0, 2, 2, 4, 3, 2 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 1, 1, 1, 0, -1, -1, -2, -2, -2 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, -4, -4, -1, -4, -1, 0 ],
[ 0, 2, 2, 0, 4, 4, 1, 4, 1, 0 ],
[ 0, -2, -2, 0, -4, -3, 0, -2, 0, 0 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ -4, -6, -6, -3, -8, -8, -4, -8, -4, -2 ],
[ 4, 6, 5, 2, 8, 6, 2, 4, 1, 0 ],
[ 4, 4, 4, 2, 4, 4, 2, 4, 2, 1 ],
[ -8, -8, -6, -2, -8, -6, -2, -4, -1, 0 ],
[ 4, 4, 2, 0, 4, 2, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, -4, -3, 0, -2, 0, 0 ],
[ 0, 0, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -2, -1, -2, -1, 0 ],
[ 1, 2, 1, 0, 4, 2, 0, 1, 0, 0 ],
[ 0, -1, 0, 0, -4, -1, 0, 0, 0, 0 ],
[ 0, 1, 1, 1, 4, 3, 2, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2 ],
ListSign := [ 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1,
-1, -1, -1, 1, 1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 1, 2, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 ],
[ -2, -2, -2, -1, -2, -2, -1, 0, 0, 0 ],
[ 2, 1, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 2, 1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -1, -3, -2, 0, -1, -1, -4, -3, -2 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
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[ 0, 0, 1, 1, 0, 0, 0, 0, 1, 2 ],
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[ 0, 1, 0, -1, 0, 0, 1, 0, 0, -2 ],
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[ 1, 0, 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
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[ 0, 0, 0, 0, 0, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, -2, -1, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ],
[ 0, 1, 0, 0, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
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[ 0, 0, 2, 2, 0, 2, 2, 4, 3, 2 ],
[ 0, 0, -2, -2, 0, -1, -1, -2, -2, -2 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -4, -4, -6, -3, -4, -6, -3, -8, -4, -2 ],
[ 4, 3, 5, 3, 2, 3, 2, 4, 3, 2 ],
[ 4, 4, 4, 2, 4, 4, 2, 4, 2, 1 ],
[ -8, -6, -6, -4, -4, -4, -3, -4, -3, -2 ],
[ 4, 2, 2, 2, 1, 1, 1, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 1, 0, 1, 0 ],
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[ 0, 1, 1, 0, 0, 1, 1, 2, 1, 0 ],
[ 1, 0, 0, 1, 0, 0, 0, 0, 0, 1 ],
[ -4, -1, -1, -3, 0, 0, -1, 0, -1, -2 ],
[ 2, 0, 1, 2, 0, 0, 0, 0, 1, 2 ],
[ 4, 2, 2, 2, 1, 1, 1, 1, 1, 1 ],
[ -4, -1, -3, -3, 0, -1, -1, -2, -2, -2 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
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[ 0, 1, 0, -1, 0, 1, 1, 0, -1, -2 ],
[ 0, 0, 0, 0, 1, 0, -1, 0, 0, 1 ] ],
[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ -2, -3, -3, -2, -4, -4, -3, -4, -3, -2 ],
[ 0, 1, 2, 1, 2, 3, 2, 4, 3, 2 ],
[ 2, 1, 0, 0, 0, -1, -1, -2, -2, -2 ],
[ 1, 2, 2, 1, 4, 4, 2, 4, 2, 1 ],
[ 0, -1, -2, -1, -4, -6, -3, -8, -4, -2 ],
[ -2, -2, -1, 0, 0, 2, 2, 4, 3, 2 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
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[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
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[ -2, -1, -2, -2, 0, -1, -1, -2, -2, -2 ],
[ 1, 0, 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 0, 1, 0, -1, 0, 0, 1, 0, 0, -2 ],
[ 2, 0, 1, 2, 0, 0, 0, 0, 1, 2 ],
[ 0, 0, 0, 0, 1, 0, -1, 0, 0, 1 ],
[ 0, 1, 0, -1, 0, 1, 1, 0, -1, -2 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 1, 0, -1, 0, 0, 0, 0, 0, 0 ],
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[ -4, -4, -1, 2, -4, -1, 2, 0, 1, 0 ],
[ 1, 1, 0, -1, 1, 0, -1, 0, 0, 1 ] ] ] ) ) ], [ rec(
TheMatrixStab :=
Group([ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ -2, -1, -2, -1, 0,
0, 0, 0, 0, 0 ], [ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
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[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
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[ 0, 0, 0, 1, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
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[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
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[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
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[ 0, 0, -2, -1, 0, -2, -1, -4, -1, 0 ],
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[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
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[ 0, 0, 0, 1, 0, 0, 0, 0, 1, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -2, 0, 0 ],
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[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -1, -2, -1, 0, -1, -1, -2, -1, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, -2, -1, 0, -2, -1, -4, -1, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, 0, 0, -2, -2, -2 ],
[ 0, 0, 2, 1, 0, 0, 0, 4, 3, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 4, 2, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, -2, -1, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, -1, -1, -2, -1, 0 ],
[ 0, 0, 0, 0, 0, 2, 1, 4, 1, 0 ],
[ 1, 1, 0, -1, 1, 0, -1, 0, 0, 1 ],
[ 0, 0, 1, 1, 0, 1, 1, 0, -1, -2 ],
[ 0, 0, -2, -1, 0, -2, -1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 4, 2, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 0, 2, 1, 0, 2, 1, 4, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ], [ 0, -1, -1, 0, -2,
-1, 0, 0, 0, 0 ], [ 0, 0, 0, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 1, 1, 0, 0, -1, -1, -2, -1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, 0 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, -2, -2, -2 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 1, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 4, 4 ],
ListSign := [ 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1,
-1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
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[ 0, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -3, -2, -4, -3, -2 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, -1, -2, -1, 0, 0,
0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, -2, -3, -2, -4, -3, -2 ],
[ 0, 0, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3,
3 ],
ListSign := [ 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1,
-1, 1, -1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -2, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -3, -2, -4, -3, -2 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -2, -2 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -2, -1, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 1, 2, 1, 0, -1, -1, -4, -3, -2 ],
[ 0, -1, -2, -1, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ],
[ -2, -1, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, -1, -1, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 1, 1, 0, 0, 0 ],
[ 0, -1, 0, 0, -2, -2, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ],
[ -2, -1, -3, -2, 0, -1, -1, -4, -3, -2 ],
[ 0, 1, 2, 1, 0, 1, 1, 4, 3, 2 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ 0, -1, -2, -1, -2, -4, -2, -8, -4, -2 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, -2 ],
[ 0, -1, -1, 0, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 2, 1, 2, 3, 2, 4, 3, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -2, -2 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 1, 2, 1, 0, -1, 0, -4, -1, 0 ],
[ 0, -1, -1, -1, 0, 1, 0, 2, 1, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, -2, -3, -2, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -2, -1, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, -1, -2, -1, 0, 1, 1, 4, 3, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -2, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, -1, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, -1, 0, 0, 0, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ] ] ) ), rec(
TheMatrixStab :=
Group([ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ -2, -1, 0, 0, 0, 0,
0, 0, 0, 0 ], [ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -2, -2, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, -1, -1, -2, -2, -2 ],
[ 0, -1, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 2, 1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 0, 0, -1, -1, -4, -3, -2 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 1, 1, 0, 0, 1, 0, 2, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, -2, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, -1, -1, -1, -2, -3, -2, -4, -3, -2 ],
[ 0, 1, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 2, 1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, -2, -3, -1, -4, -1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 1, 0, 1, 0 ],
[ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, -1, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 0, -1, -1, -2, -2, -2 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 2, 2 ],
[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 1, 1, 1, 0, 1, 0, 2, 1, 0 ],
[ -2, -1, -2, -1, 0, -1, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, -1, -1, -1, -2, -2, -2, -2, -2, -2 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -1, -2, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, -1, -1, -1, -2, -2, -1, -2, -1, 0 ],
[ 0, 1, 2, 1, 2, 3, 1, 4, 1, 0 ],
[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 1, 1, 1, 0, 1, 0, 2, 1, 0 ],
[ 0, -1, -2, -1, 0, -1, 0, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 0, 0, 0, 0, -2, -3, -2, -4, -3, -2 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -2, -1, -2, -3, -1, -4, -1, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 2, 2, 1, 2, 2, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -2, -1, -2, -3, -2, -4, -3, -2 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 0, -1,
0, -4, -1, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 2, 1, 0 ],
[ 1, 1, 2, 1, 1, 2, 1, 4, 2, 1 ],
[ -2, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 1, 0, 0, -1, -1, -4, -3, -2 ],
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[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
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[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, 0, 0 ],
[ 0, 1, 0, 0, 0, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, -2, -3, -1, -4, -1, 0 ],
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[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
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[ 0, 0, 0, 0, 0, -1, -1, -2, -1, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
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[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 0, 0, 0 ],
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[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, -2, -2, 0, -2, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 4, 1, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, 0, 0, -2, -2, -2 ],
[ 0, 1, 2, 1, 0, 1, 1, 4, 3, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, -2, -1, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, -1, 0, -2, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
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[ 0, 0, 1, 1, 0, 0, 0, -2, -1, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, -1, 0, -2, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 2, 1, 0 ],
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[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, 0, 1, 1, 2, 1, 0 ],
[ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ],
[ -2, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 2, 0, 0, -1, 0, 0, 0, -2, -1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, 1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, -2, -1, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, -1, 0, -2, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
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[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ],
[ -2, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 2, 1, 0, 1, 1, 2, 1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ],
[ -2, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 2, 1, 0, 1, 1, 2, 1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -2, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 0, -1, -1, -2, -1, 0 ],
[ 0, 0, 0, 0, 0, 1, 1, 4, 2, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, -2, -2, 0, -2, 0, 0 ],
[ 0, 1, 2, 0, 2, 3, 0, 4, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -3, 0, -4, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 0, 4, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ],
[ -2, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 2, 1, 0, 1, 1, 2, 1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ] ] ]),
TheRotSubgroup :=
Group([ [ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ], [ 0, 0, -1, 0, 0, -1,
0, -2, 0, 0 ], [ 0, 0, 0, 0, 0, 1, 0, 2, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, 0, -4, -1, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, -2, -2, 0, -2, 0, 0 ],
[ 0, 1, 2, 1, 2, 3, 1, 4, 1, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ],
[ -2, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 2, 1, 0, 1, 1, 2, 1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 1, 0, 2, 0, 0 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ],
[ -2, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 2, -1, -2, -1, 0, 1, 1, 2, 1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 1, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, -1, -1, 0, 1, 1, 0, 1, 0, 0 ] ] ]),
BoundaryImage := rec(
ListIFace := [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3 ]
,
ListSign := [ 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1,
-1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1,
1, -1, 1, 1, -1, 1 ],
ListElt :=
[ [ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0, 0,
0, 0, 0 ], [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, -1, -1, -2, -1, 0 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 2, 1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, -1, -1, 0, -2, -2, 0, -2, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 1, 1, 2, 1, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, -2, -1, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, -1, 0, -2, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, -1, -2 ],
[ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, -1, 0, 0, -1, 0, -2, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 2, 1, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, -1, 0, -1, -1, -2, -1, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, -1, 0, -1, -1, -2, -1, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ],
[ -2, 0, 1, 0, 0, 0, 0, 0, 0, 0 ],
[ 2, 1, 0, 0, 0, -1, 0, -2, 0, 0 ],
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ -2, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 1, 1, 1, 0, 1, 1, 0, 1, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 4, 1, 0 ],
[ 1, 0, 1, 1, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, -1, -1, 0, 0, 0, -2, -2, -2 ],
[ 0, 1, 2, 1, 0, 1, 1, 4, 3, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, -1, -1, -4, -3, -2 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, -1, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, 0, 0, 1, 0, -1, 0, 0, 1 ],
[ 0, 0, 0, 0, 0, 1, 1, 0, -1, -2 ],
[ 0, 1, 0, -1, 0, -1, -1, 0, 1, 2 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 1, 1, 0, 0, 0, -2, -2, -2 ],
[ 1, 0, -1, -1, 0, 0, 0, 1, 1, 1 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 2, 1, 4, 2, 1 ],
[ 0, 0, 0, 0, -2, -3, -1, -4, -1, 0 ],
[ 0, 0, 0, 0, 2, 2, 1, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 1, 0, 1, 0, 0 ],
[ 0, 0, 0, 0, -2, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ] ],
[ [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 0, 0, 0, 0, 0, -1, -1, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, -2, -1, 0 ],
[ 0, 0, -1, -1, 0, 0, 0, 2, 1, 0 ],
[ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ],
[ 0, 1, 0, 0, 0, -1, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ],
[ 0, 0, 1, 0, 0, 0, 0, -2, 0, 0 ],
[ 1, 0, -1, 0, 0, 0, 0, 1, 0, 0 ] ],
[ [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, -1, 0, 0, 0, 0, 0, 0, 0, 0 ],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ],
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