The conjecture:
the edge-vertex graph of an n-facet polytope in d-dimensional Euclidean space has diameter no more than n − d.The result:
I will describe the construction of a 43-dimensional polytope with 86 facets and diameter bigger than 43. The proof is based on a generalization of the d-step theorem of Klee and Walkup.
The proof will be presented at the 100 Years in Seattle (The mathematics of Klee and Grunbaum) conference in end-July, this year.
