CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutSign UpSign In

Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place.

| Download

GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

Views: 418384
HAP_GCOMPLEX_SETUP:=[false]; 
HAP_GCOMPLEX_LIST:=[[rec(TheMatrixStab:=Group([ [ [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ], [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ] ], 
  [ [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ], [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ] ], 
  [ [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ], [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ] ], 
  [ [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ], [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ] ], 
  [ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ] ], 
  [ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ] ], 
  [ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ] ], 
  [ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ] ], 
  [ [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ], [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ] ], 
  [ [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ], [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ] ], 
  [ [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ] ], 
  [ [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ], [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ] ], 
  [ [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ], [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ] ], 
  [ [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ], [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ] ], 
  [ [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ], [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ] ], 
  [ [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ], [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ] ], 
  [ [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ], [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ] ], 
  [ [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ], [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ] ], 
  [ [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], 
  [ [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ], [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ] ], 
  [ [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ], [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ] ], 
  [ [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ], [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ] ], 
  [ [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ], [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ] ], 
  [ [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ], [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ] ], 
  [ [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ], [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ] ], 
  [ [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ], [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ] ], 
  [ [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ], [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ] ], 
  [ [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ], [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ] ], 
  [ [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ], [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ] ], 
  [ [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ], [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ] ], 
  [ [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ], [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ] ], 
  [ [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ], [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ] ], 
  [ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ], [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ] ], 
  [ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ], [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ] ], 
  [ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ] ], 
  [ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ] ], 
  [ [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ], [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ] ], 
  [ [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ], [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ] ], 
  [ [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ], [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ] ], 
  [ [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], 
  [ [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ], [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ] ], 
  [ [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ], [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ] ], 
  [ [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ], [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ] ], 
  [ [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ], [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ], 
  [ [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ], [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ] ], 
  [ [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ], [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ] ], 
  [ [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ] ], 
  [ [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ], [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ] ], 
  [ [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ], [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ] ], 
  [ [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ], [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ] ], 
  [ [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ], [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ], 
  [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ] ], 
  [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ] ], 
  [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ] ], 
  [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ] ], 
  [ [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ], [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ] ], 
  [ [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ], [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ] ], 
  [ [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ], [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ] ], 
  [ [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ], [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ] ], 
  [ [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ] ], 
  [ [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ], [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ] ], 
  [ [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ], [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ], 
  [ [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ], [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ] ], 
  [ [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ], [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ] ], 
  [ [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ], [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ] ], 
  [ [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ], [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ] ], 
  [ [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ], [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ] ], 
  [ [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], 
  [ [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ], [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ] ], 
  [ [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ], 
  [ [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ], [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ] ], 
  [ [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ], [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ] ], 
  [ [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ], [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ] ], 
  [ [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ], [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ] ], 
  [ [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ], [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ] ], 
  [ [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ], [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ] ], 
  [ [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ], [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ] ], 
  [ [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ], [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ] ], 
  [ [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ], [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ], 
  [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ], [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ] ], 
  [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ], [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ] ], 
  [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ], [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ] ], 
  [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ], 
  [ [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ], [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ] ], 
  [ [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ], [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ] ], 
  [ [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ], [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ] ], 
  [ [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ], [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ] ], 
  [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ] ], 
  [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], 
  [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ] ], 
  [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ] ], 
  [ [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ], [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ] ], 
  [ [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ], [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ], 
  [ [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ], [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ] ], 
  [ [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ] ]),TheRotSubgroup:=Group([ [ [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ], [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ] ], 
  [ [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ], [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ] ], 
  [ [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ], [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ] ], 
  [ [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ], [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ] ], 
  [ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ] ], 
  [ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ] ], 
  [ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ] ], 
  [ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ] ], 
  [ [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ], [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ] ], 
  [ [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ], [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ] ], 
  [ [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ] ], 
  [ [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ], [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ] ], 
  [ [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ], [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ] ], 
  [ [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ], [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ] ], 
  [ [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ], [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ] ], 
  [ [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ], [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ] ], 
  [ [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ], [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ] ], 
  [ [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ], [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ] ], 
  [ [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], 
  [ [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ], [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ] ], 
  [ [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ], [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ] ], 
  [ [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ], [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ] ], 
  [ [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ], [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ] ], 
  [ [ -1, 1, 1, 0 ], [ -1, -1, 0, 1 ], [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ] ], 
  [ [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ], [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ] ], 
  [ [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ], [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ] ], 
  [ [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ], [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ] ], 
  [ [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ], [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ] ], 
  [ [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ], [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ] ], 
  [ [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ], [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ] ], 
  [ [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ], [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ] ], 
  [ [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ], [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ] ], 
  [ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ], [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ] ], 
  [ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ], [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ] ], 
  [ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ] ], 
  [ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ] ], 
  [ [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ], [ -1, -1, 0, 1 ], [ 1, -1, -1, 0 ] ], 
  [ [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ], [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ] ], 
  [ [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ], [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ] ], 
  [ [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], 
  [ [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ], [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ] ], 
  [ [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ], [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ] ], 
  [ [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ], [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ] ], 
  [ [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ], [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ], 
  [ [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ], [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ] ], 
  [ [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ], [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ] ], 
  [ [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ] ], 
  [ [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ], [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ] ], 
  [ [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ], [ -1, 0, 1, 1 ], [ 0, -1, -1, 1 ] ], 
  [ [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ], [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ] ], 
  [ [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ], [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ] ], 
  [ [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ], 
  [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ -1, 0, 1, 0 ], [ 0, -1, 0, 1 ] ], 
  [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ] ], 
  [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ] ], 
  [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ] ], 
  [ [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ], [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ] ], 
  [ [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ], [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ] ], 
  [ [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ], [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ] ], 
  [ [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ], [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ] ], 
  [ [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ] ], 
  [ [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ], [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ] ], 
  [ [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ], [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ], 
  [ [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ], [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ] ], 
  [ [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ], [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ] ], 
  [ [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ], [ 0, 1, 0, -1 ], [ -1, 0, 1, 0 ] ], 
  [ [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ], [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ] ], 
  [ [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ], [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ] ], 
  [ [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], 
  [ [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ], [ 0, 1, 1, -1 ], [ -1, 0, 1, 1 ] ], 
  [ [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ], 
  [ [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ], [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ] ], 
  [ [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ], [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ] ], 
  [ [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ], [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ] ], 
  [ [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ], [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ] ], 
  [ [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ], [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ] ], 
  [ [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ], [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ] ], 
  [ [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ], [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ] ], 
  [ [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ], [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ] ], 
  [ [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ], [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ], 
  [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ], [ 0, -1, -1, 1 ], [ 1, 0, -1, -1 ] ], 
  [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ], [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ] ], 
  [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ], [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ] ], 
  [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ], 
  [ [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ], [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ] ], 
  [ [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ], [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ] ], 
  [ [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ], [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ] ], 
  [ [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ], [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ] ], 
  [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, -1, 0, 1 ], [ 1, 0, -1, 0 ] ], 
  [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], 
  [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 1, -1, -1, 0 ], [ 1, 1, 0, -1 ] ], 
  [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ] ], 
  [ [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ], [ 1, 0, -1, -1 ], [ 0, 1, 1, -1 ] ], 
  [ [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ], [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ], 
  [ [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ], [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ] ], 
  [ [ 1, 1, 0, -1 ], [ -1, 1, 1, 0 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ] ]),BoundaryImage:=rec(ListIFace:=[  ],ListSign:=[  ],ListElt:=[  ]))],[rec(TheMatrixStab:=Group([ [ [ -2, -1, 1, 2 ], [ 1, -2, -2, 1 ], [ -2, 0, 2, 1 ], [ 0, -2, -1, 2 ] ], 
  [ [ -2, 0, 2, 1 ], [ 0, -2, -1, 2 ], [ -2, 1, 2, 0 ], [ -1, -2, 0, 2 ] ], 
  [ [ -2, 1, 2, 0 ], [ -1, -2, 0, 2 ], [ -1, 2, 2, -1 ], [ -2, -1, 1, 2 ] ], 
  [ [ -1, -2, 0, 2 ], [ 2, -1, -2, 0 ], [ -2, -1, 1, 2 ], [ 1, -2, -2, 1 ] ], 
  [ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ] ], 
  [ [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ], [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ] ], 
  [ [ -1, 2, 2, -1 ], [ -2, -1, 1, 2 ], [ 0, 2, 1, -2 ], [ -2, 0, 2, 1 ] ], 
  [ [ 0, -2, -1, 2 ], [ 2, 0, -2, -1 ], [ -1, -2, 0, 2 ], [ 2, -1, -2, 0 ] ], 
  [ [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ], [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ] ], 
  [ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ] ], 
  [ [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ], [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ] ], 
  [ [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ], [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ] ], 
  [ [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ], [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ] ], 
  [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ] ], 
  [ [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ] ], 
  [ [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ], 
  [ [ 0, 2, 1, -2 ], [ -2, 0, 2, 1 ], [ 1, 2, 0, -2 ], [ -2, 1, 2, 0 ] ], 
  [ [ 1, -2, -2, 1 ], [ 2, 1, -1, -2 ], [ 0, -2, -1, 2 ], [ 2, 0, -2, -1 ] ], 
  [ [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ], [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ] ], 
  [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], 
  [ [ 1, 2, 0, -2 ], [ -2, 1, 2, 0 ], [ 2, 1, -1, -2 ], [ -1, 2, 2, -1 ] ], 
  [ [ 2, -1, -2, 0 ], [ 1, 2, 0, -2 ], [ 1, -2, -2, 1 ], [ 2, 1, -1, -2 ] ], 
  [ [ 2, 0, -2, -1 ], [ 0, 2, 1, -2 ], [ 2, -1, -2, 0 ], [ 1, 2, 0, -2 ] ], 
  [ [ 2, 1, -1, -2 ], [ -1, 2, 2, -1 ], [ 2, 0, -2, -1 ], [ 0, 2, 1, -2 ] ] ]),TheRotSubgroup:=Group([ [ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ] ], 
  [ [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ], [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ] ], 
  [ [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ], [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ] ], 
  [ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ] ], 
  [ [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ], [ -1, 0, 0, 1 ], [ 0, -1, -1, 0 ] ], 
  [ [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ], [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ] ], 
  [ [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ], [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ] ], 
  [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ] ], 
  [ [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ] ], 
  [ [ 0, 1, 1, 0 ], [ -1, 0, 0, 1 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ], 
  [ [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ], [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ] ], 
  [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ] ]),BoundaryImage:=rec(ListIFace:=[ 1, 1 ],ListSign:=[ -1, 1 ],ListElt:=[ [ [ 1, 0, 0, -1 ], [ 0, 1, 1, 0 ], [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ] ], 
  [ [ -1, 1, 0, -1 ], [ -1, -1, 1, 0 ], [ 0, 1, -1, -1 ], [ -1, 0, 1, -1 ] ] ]))],[rec(TheMatrixStab:=Group([ [ [ -3, 0, 2, 2 ], [ 0, -3, -2, 2 ], [ -2, 2, 3, 0 ], [ -2, -2, 0, 3 ] ], 
  [ [ -2, -2, 0, 3 ], [ 2, -2, -3, 0 ], [ -3, 0, 2, 2 ], [ 0, -3, -2, 2 ] ], 
  [ [ -2, -1, 0, 2 ], [ 1, -2, -2, 0 ], [ -2, 0, 1, 2 ], [ 0, -2, -2, 1 ] ], 
  [ [ -2, 0, 1, 2 ], [ 0, -2, -2, 1 ], [ -1, 2, 2, 0 ], [ -2, -1, 0, 2 ] ], 
  [ [ -2, 0, 2, 1 ], [ 0, -2, -1, 2 ], [ -2, 1, 2, 0 ], [ -1, -2, 0, 2 ] ], 
  [ [ -2, 1, 2, 0 ], [ -1, -2, 0, 2 ], [ 0, 2, 1, -2 ], [ -2, 0, 2, 1 ] ], 
  [ [ -2, 2, 3, 0 ], [ -2, -2, 0, 3 ], [ 0, 3, 2, -2 ], [ -3, 0, 2, 2 ] ], 
  [ [ -1, -2, 0, 2 ], [ 2, -1, -2, 0 ], [ -2, 0, 2, 1 ], [ 0, -2, -1, 2 ] ], 
  [ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ] ], 
  [ [ -1, 2, 2, 0 ], [ -2, -1, 0, 2 ], [ 0, 2, 2, -1 ], [ -2, 0, 1, 2 ] ], 
  [ [ 0, -3, -2, 2 ], [ 3, 0, -2, -2 ], [ -2, -2, 0, 3 ], [ 2, -2, -3, 0 ] ], 
  [ [ 0, -2, -2, 1 ], [ 2, 0, -1, -2 ], [ -2, -1, 0, 2 ], [ 1, -2, -2, 0 ] ], 
  [ [ 0, -2, -1, 2 ], [ 2, 0, -2, -1 ], [ -1, -2, 0, 2 ], [ 2, -1, -2, 0 ] ], 
  [ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ] ], 
  [ [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ], [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ] ], 
  [ [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ], [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ] ], 
  [ [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ], 
  [ [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ], [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ] ], 
  [ [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ] ], 
  [ [ 0, 2, 1, -2 ], [ -2, 0, 2, 1 ], [ 1, 2, 0, -2 ], [ -2, 1, 2, 0 ] ], 
  [ [ 0, 2, 2, -1 ], [ -2, 0, 1, 2 ], [ 2, 1, 0, -2 ], [ -1, 2, 2, 0 ] ], 
  [ [ 0, 3, 2, -2 ], [ -3, 0, 2, 2 ], [ 2, 2, 0, -3 ], [ -2, 2, 3, 0 ] ], 
  [ [ 1, -2, -2, 0 ], [ 2, 1, 0, -2 ], [ 0, -2, -2, 1 ], [ 2, 0, -1, -2 ] ], 
  [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], 
  [ [ 1, 2, 0, -2 ], [ -2, 1, 2, 0 ], [ 2, 0, -2, -1 ], [ 0, 2, 1, -2 ] ], 
  [ [ 2, -2, -3, 0 ], [ 2, 2, 0, -3 ], [ 0, -3, -2, 2 ], [ 3, 0, -2, -2 ] ], 
  [ [ 2, -1, -2, 0 ], [ 1, 2, 0, -2 ], [ 0, -2, -1, 2 ], [ 2, 0, -2, -1 ] ], 
  [ [ 2, 0, -2, -1 ], [ 0, 2, 1, -2 ], [ 2, -1, -2, 0 ], [ 1, 2, 0, -2 ] ], 
  [ [ 2, 0, -1, -2 ], [ 0, 2, 2, -1 ], [ 1, -2, -2, 0 ], [ 2, 1, 0, -2 ] ], 
  [ [ 2, 1, 0, -2 ], [ -1, 2, 2, 0 ], [ 2, 0, -1, -2 ], [ 0, 2, 2, -1 ] ], 
  [ [ 2, 2, 0, -3 ], [ -2, 2, 3, 0 ], [ 3, 0, -2, -2 ], [ 0, 3, 2, -2 ] ], 
  [ [ 3, 0, -2, -2 ], [ 0, 3, 2, -2 ], [ 2, -2, -3, 0 ], [ 2, 2, 0, -3 ] ] ]),TheRotSubgroup:=Group([ [ [ -3, 0, 2, 2 ], [ 0, -3, -2, 2 ], [ -2, 2, 3, 0 ], [ -2, -2, 0, 3 ] ], 
  [ [ -2, -1, 0, 2 ], [ 1, -2, -2, 0 ], [ -2, 0, 1, 2 ], [ 0, -2, -2, 1 ] ], 
  [ [ -2, 1, 2, 0 ], [ -1, -2, 0, 2 ], [ 0, 2, 1, -2 ], [ -2, 0, 2, 1 ] ], 
  [ [ -1, -2, 0, 2 ], [ 2, -1, -2, 0 ], [ -2, 0, 2, 1 ], [ 0, -2, -1, 2 ] ], 
  [ [ -1, 0, 0, 0 ], [ 0, -1, 0, 0 ], [ 0, 0, -1, 0 ], [ 0, 0, 0, -1 ] ], 
  [ [ -1, 2, 2, 0 ], [ -2, -1, 0, 2 ], [ 0, 2, 2, -1 ], [ -2, 0, 1, 2 ] ], 
  [ [ 0, -3, -2, 2 ], [ 3, 0, -2, -2 ], [ -2, -2, 0, 3 ], [ 2, -2, -3, 0 ] ], 
  [ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ] ], 
  [ [ 0, 1, 0, 0 ], [ -1, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ] ], 
  [ [ 0, 3, 2, -2 ], [ -3, 0, 2, 2 ], [ 2, 2, 0, -3 ], [ -2, 2, 3, 0 ] ], 
  [ [ 1, -2, -2, 0 ], [ 2, 1, 0, -2 ], [ 0, -2, -2, 1 ], [ 2, 0, -1, -2 ] ], 
  [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ], 
  [ [ 1, 2, 0, -2 ], [ -2, 1, 2, 0 ], [ 2, 0, -2, -1 ], [ 0, 2, 1, -2 ] ], 
  [ [ 2, -1, -2, 0 ], [ 1, 2, 0, -2 ], [ 0, -2, -1, 2 ], [ 2, 0, -2, -1 ] ], 
  [ [ 2, 1, 0, -2 ], [ -1, 2, 2, 0 ], [ 2, 0, -1, -2 ], [ 0, 2, 2, -1 ] ], 
  [ [ 3, 0, -2, -2 ], [ 0, 3, 2, -2 ], [ 2, -2, -3, 0 ], [ 2, 2, 0, -3 ] ] ]),BoundaryImage:=rec(ListIFace:=[ 1, 1, 1, 1 ],ListSign:=[ 1, -1, -1, -1 ],ListElt:=[ [ [ 0, 0, 0, 1 ], [ 0, 0, -1, 0 ], [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ] ], 
  [ [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ], [ 0, -1, -1, 0 ], [ 1, 0, 0, -1 ] ], 
  [ [ 0, 2, 0, -1 ], [ -2, 0, 1, 0 ], [ 1, 2, 0, -1 ], [ -2, 1, 1, 0 ] ], 
  [ [ 2, 2, -1, -2 ], [ -2, 2, 2, -1 ], [ 3, 0, -2, -1 ], [ 0, 3, 1, -2 ] ] ]))]];