Can two non-equivalent polytopes of same dimension have the same graph?

The 1-skeleton is usually not enough to recover the face lattice, but under some conditions it is. I did a quick google search, and read the abstract in this paper.


There are many non-equivalent neighborly polytopes, already in dimension $d=4$. See for example

  • Arnau Padrol. "Many Neighborly Polytopes and Oriented Matroids"

Tags:

Graph Theory

Discrete Geometry

Convex Polytopes

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