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Can the graph of a symmetric polytope have more symmetries than the polytope itself?

The answer is No, the graph of an arc-transitive polytope cannot have more symmetries than the polytope. The polytope and its graph have the exact same symmetries! In the article "Capturing ...
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1 vote

4D Duoprisms based on nonconvex polygons

The great duoantiprism can be constructed using a compound of two pentagonal-pentagrammic duoprisms by inserting additional edges, or by alternating a decagonal-decagrammic duoprism.
5 votes

In a set of n points on $R^d$, each point can be "well separated" from the rest by a linear functional. Is the dimension necessarily $\Omega(n)$?

Take all the vectors of the form $e_i+e_j$, $i\neq j$, where $e_1,\dots,e_d$ is a base in $\mathbb R^d$. They satisfy your requirements, the vector $e_i+e_j$ being separated from the others by $e_i^*+...

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