3719.sagews

def Line(i, n=5):
    return line([(cos(pi*i/n),sin(pi*i/n)), (-cos(pi*i/(n+1)),-sin(pi*i/(n+1)))])

def Cuts(n):
    return sum(Line(i, n) for i in range(n))

def Demo(n, m=0):
    for i in range(1, n):
        x = -1+2*i/(n+1)
        yield line([(x, 1), (x, -1)])
    x = -1+2*n/(n+1)
    yield line([(x, 1), (x-2*m/n, -1)])
        
        
Dessin1 = [circle((0, 0), 1) + Cuts(i) for i in range(6)]
Dessin2 = [circle((0, 0), 1) + sum(Demo(5, i)) for i in range(5)]
Dessin3 = [circle((0, 0), 1) + sum(Demo(i)) for i in range(1, 6)]
Dessin1 + Dessin2 + Dessin3

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colors = ['red', 'green', 'blue', 'yellow', 'purple']

def b(i, n):
    return i / (n + 1) if i > -1 else 1

def d(i, n):
    return (n - 1)**(i - 2) / (n + 1) if i else 0

def Function(i, n):
    return lambda x, y: (1 - d(i, n) - b(i, n)) * x - (1 - d(i-1, n) - b(i-1, n)) * y + b(i, n)

def Plane(i, n):
    f = Function(i, n)
    return plot3d(f, (-1.5, 1.5), (-1.5, 1.5), color=colors[i%len(colors)], opacity=0.6)

def Planes(n):
    return sum(Plane(i, n) for i in range(n))
    
Cube = cube((0, 0, 0), 2, opacity=0.3)

Cube + Planes(4)

Cube + Planes(5)