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asked 2014-07-03 03:20:12 -0500

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combinatorial equivalence for Polyhedra / isomorphism for lattices

Is there an easy way to check whether two polyhedra are combinatorial equivalent, i.e. have have isomorphic face lattices.

this does not work:

Poly1=Polyhedron(vertices=[[0,1],[1,0],[1,1]], base_ring=QQ)
Poly2=Polyhedron(vertices=[[2,0],[2,2],[0,2]], base_ring=QQ)
Poly1.face_lattice()==Poly2.face_lattice()

In this case this would work:

str(Poly1.faces(1))==str(Poly2.faces(1))

but what would be a good way to check this in general?

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combinatorial equivalence for Polyhedra / isomorphism for lattices

Is there an easy way to check whether two polyhedra are combinatorial equivalent, i.e. have have isomorphic face lattices.

this does not work:

Poly1=Polyhedron(vertices=[[0,1],[1,0],[1,1]], base_ring=QQ)
Poly2=Polyhedron(vertices=[[2,0],[2,2],[0,2]], base_ring=QQ)
Poly1.face_lattice()==Poly2.face_lattice()

In this case this would work:

str(Poly1.faces(1))==str(Poly2.faces(1))

but what would be a good way to check this in general?

click to hide/show revision 3
retagged

combinatorial equivalence for Polyhedra / isomorphism for lattices

Is there an easy way to check whether two polyhedra are combinatorial equivalent, i.e. have have isomorphic face lattices.

this does not work:

Poly1=Polyhedron(vertices=[[0,1],[1,0],[1,1]], base_ring=QQ)
Poly2=Polyhedron(vertices=[[2,0],[2,2],[0,2]], base_ring=QQ)
Poly1.face_lattice()==Poly2.face_lattice()

In this case this would work:

str(Poly1.faces(1))==str(Poly2.faces(1))

but what would be a good way to check this in general?