Tagged Questions

An "abstract polytope" is a poset satisfying a list of properties shared by face lattices of polytopes.

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1answer
86 views

Criteria for abstract polytopes to be convex polytope

Suppose I have an abstract polytope defined by a poset. Are there any methods for determining whether the abstract polytope can be geometrically realized as convex-hull on its set of vertices?
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2answers
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Build a topological polytope with a specified CW-structure

I am a topologist and not quite familiar with the tools for building a polytope. I would like to build some topological polytope which is an somewhere in between permutohedron and associahedron which ...
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1answer
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Labeled polytopes

In a "problem of a week" contest in my school, I gave the following problem to students: we assign to each vertex of a cube a number $1$ or $-1$. And we associate to each face the product of the ...
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0answers
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What's the best way to test if a sphere is a polytope? (algorithms for the Simplicial Steinitz Problem)

The problem of recognizing whether a simplicial face lattice is polytopal is sometimes called the Steinitz problem. Sturmfels and Bokowski advanced a set of methods in the late 80s to test whether ...
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3answers
941 views

Which finite groups are generated by n involutions?

One of the interesting problems in abstract polytope theory is to determine, for a given finite group, when that group is the automorphism group of a regular abstract polytope. This is equivalent to ...