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var("x y z")
P = vector((x,y,z))

eqns  = [ x==-1, x==1, y==-1, y==1, z==-1, z==1 ]
#eqns  = [ z==0, x+y+z ==1, -x+y+z == 1, -x-y+z==1, x-y+z==1]

indizes = range(len(eqns))

vertices = []
for C in combinations(indizes,3):
    lse = [eqns[i] for i in C]
    sol = solve(lse,x,y,z,solution_dict=True)

    if sol:
        vertices.append(P.substitute(sol[0]))

#for V in vertices:    print V  

"draw the solid start with vertices"        
G = point3d(vertices,size=10,color='red')

" faces "
for eq in eqns:
    poly = []
    for V in vertices:
        if(eq.substitute({x:V[0],y:V[1],z:V[2]})):
            if not V in poly:
                poly.append(V)

    """TODO    poly should be convex"""
    shuffle(poly)
    # print poly
    try:
        G += polygon(poly,alpha=0.5,color=(random(),random(),random()))
    except:
        pass

G.show(aspect_ratio=1)

var("x y z")
P = vector((x,y,z))

eqns  = [ x==-1, x==1, y==-1, y==1, z==-1, z==1 ]
#eqns  = [ z==0, x+y+z ==1, -x+y+z == 1, -x-y+z==1, x-y+z==1]

indizes = range(len(eqns))

vertices = []
for C in combinations(indizes,3):
    lse = [eqns[i] for i in C]
    sol = solve(lse,x,y,z,solution_dict=True)
     if sol:
        vertices.append(P.substitute(sol[0]))

#for V in vertices:    print V  

"draw the solid  - start with vertices"        
G = point3d(vertices,size=10,color='red')

" faces "
for eq in eqns:
    poly = []
    for V in vertices:
        if(eq.substitute({x:V[0],y:V[1],z:V[2]})):
            if not V in poly:
                poly.append(V)

    """TODO    poly should be convex"""
    shuffle(poly)
    # print poly
    try:
        G += polygon(poly,alpha=0.5,color=(random(),random(),random()))
    except:
        pass

G.show(aspect_ratio=1)

var("x y z")
 P = vector((x,y,z))

eqns  = [ x==-1, x==1, y==-1, y==1, z==-1, z==1 ]
#eqns  = [ z==0, x+y+z ==1, -x+y+z == 1, -x-y+z==1, x-y+z==1]

indizes = range(len(eqns))

vertices = []
for C in combinations(indizes,3):
    lse = [eqns[i] for i in C]
    sol = solve(lse,x,y,z,solution_dict=True)
    if sol:
        vertices.append(P.substitute(sol[0]))

#for V in vertices:    print V  

"draw the solid  - start with vertices"        
G = point3d(vertices,size=10,color='red')

" faces "
for eq in eqns:
    poly = []
    for V in vertices:
        if(eq.substitute({x:V[0],y:V[1],z:V[2]})):
            if not V in poly:
                poly.append(V)

    """TODO    poly should be convex"""
    shuffle(poly)
    # print poly
    try:
        G += polygon(poly,alpha=0.5,color=(random(),random(),random()))
    except:
        pass

G.show(aspect_ratio=1)