An Euler characteristic proof that 4-prismatoids have width at most 4

TL;DR

This paper proves that 4-prismatoids cannot serve as counterexamples to the Hirsch conjecture by showing they have width at most 4, using an Euler characteristic argument.

Contribution

It provides a novel Euler characteristic proof that 4-prismatoids have bounded width, ruling out their use as counterexamples in dimension four.

Findings

4-prismatoids have width at most 4

No 4-dimensional analogue of 5-prismatoids exists as a counterexample

Euler characteristic methods are effective in this geometric context

Abstract

We show that there is no 4-dimensional analogue of the 5-prismatoids used in Santos' recent counterexample to the Hirsch conjecture.