there are someone who's working on it...

http://www.readwriteweb.com/archives/the_hirsch_conjecture_disproved.php

<< Santos, Francisco (University of Cantabria, Spain) A counter-example to the Hirsch conjecture

Victor Klee came to the Department of Mathematics to talk to me. We had a nice conversation during which he asked "Why don't you try to disprove the Hirsch Conjecture?" This talk is the answer to that question.

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. >>

copy paste from: https://sites.google.com/a/alaska.edu/kleegrunbaum/home/abstracts#Santos

best regards.

J.R.!

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