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Isomorphisms of 2-skeletons of polytopes

asked 2015-08-13 02:19:02 -0600

guillermo gravatar image

Hi there,

We are interested in checking whether the 2-skeletons of two distinct polytopes are isomorphic (as posets). We understand that we can get the face_lattice of each of the polytope, but we don't know who to produce a poset which contains the 2-skeleton for each polytope so that we can use the function is_isomorphic for posets?

Thank you in advance, and regards, Guillermo

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answered 2015-08-13 02:39:28 -0600

tmonteil gravatar image

You can restrict the face_lattice poset by using the subposet method to restrict the poset to elements corresponding to 0-faces, 1-faces and 2-faces as follows: if P is your polytope, you can do:

sage: PP = P.face_lattice()
sage: P2 = PP.subposet(P.faces(0)+P.faces(1)+P.faces(2))

Then, if you do the same with another polytope Q, you can then check:

sage: P2.is_isomorphic(Q2)
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It could make sense to have a .skeleton() method, by the way...

Nathann gravatar imageNathann ( 2015-08-13 02:43:20 -0600 )edit

Great! Thanks a lot.

guillermo gravatar imageguillermo ( 2015-08-13 02:57:28 -0600 )edit

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Asked: 2015-08-13 02:19:02 -0600

Seen: 58 times

Last updated: Aug 13 '15