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4 votes
2 answers
254 views

Does the edge-graph of a centrally symmetric polytope determine which vertices are antipodal?

Given two origin symmetric convex polytopes $P_1$ and $P_2$ (that is $P_i=-P_i$) with the same edge-graph, but potentially of different dimensions and combinatorial types. Let $\phi: G_{P_1}\to G_{P_2}...
4 votes
0 answers
132 views

Can a polytopal graph be "centrally symmetric" in more than one way?

Let $P,Q$ be two centrally symmetric convex polytopes, potentially of different dimensions and combinatorial type, but with the same edge-graph $G$. The central symmetry of $P$ induces an involutory ...
3 votes
1 answer
179 views

When is a $k$-distance-transitive graph already distance-transitive?

Call a (finite and connected) graph $k$-distance-transitive if its symmetry group acts transitively on the pairs in each one of the sets $$D_\delta:=\{(i,j)\in V\times V\mid \mathrm d(i,j)=\delta\},\...