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clarified what I meant by "characterize"
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MrB
MrB
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Extra information Information needed to distinguish combinatorially isomorphic polytopes (up to affine equivalence)

I originally posted this question on Stack Exchange, thinking it perhaps does not qualify as "research-level" but it received no answers... hopefully someone here can help.

The title pretty much sums up the question: what extra information do we need (or what is an example of sufficient information) on top of the face lattice in order to completely characterize a convex polytope, up to affine transformations? For example, would it be sufficient to provide a list of normal vectors associated with each facet for some embedding in $\mathbb{R}^d$?

Extra information needed to distinguish combinatorially isomorphic polytopes

I originally posted this question on Stack Exchange, thinking it perhaps does not qualify as "research-level" but it received no answers... hopefully someone here can help.

The title pretty much sums up the question: what extra information do we need (or what is an example of sufficient information) on top of the face lattice in order to completely characterize a convex polytope? For example, would it be sufficient to provide a list of normal vectors associated with each facet for some embedding in $\mathbb{R}^d$?

Information needed to distinguish combinatorially isomorphic polytopes (up to affine equivalence)

I originally posted this question on Stack Exchange, thinking it perhaps does not qualify as "research-level" but it received no answers... hopefully someone here can help.

The title pretty much sums up the question: what extra information do we need (or what is an example of sufficient information) on top of the face lattice in order to characterize a convex polytope, up to affine transformations? For example, would it be sufficient to provide a list of normal vectors associated with each facet for some embedding in $\mathbb{R}^d$?

Source Link
MrB
MrB
  • 399
  • 2
  • 4
  • 13

Extra information needed to distinguish combinatorially isomorphic polytopes

I originally posted this question on Stack Exchange, thinking it perhaps does not qualify as "research-level" but it received no answers... hopefully someone here can help.

The title pretty much sums up the question: what extra information do we need (or what is an example of sufficient information) on top of the face lattice in order to completely characterize a convex polytope? For example, would it be sufficient to provide a list of normal vectors associated with each facet for some embedding in $\mathbb{R}^d$?