The flip-graph of the 4-dimensional cube is connected

TL;DR

This paper proves that the flip-graph of the 4-dimensional cube's vertices is connected, revealing the structure and symmetry classes of its triangulations, totaling over 92 million.

Contribution

It establishes the connectedness of the flip-graph for the 4D cube and details the number and symmetry classes of its triangulations.

Findings

Flip-graph of the 4D cube is connected.

92,487,256 triangulations identified.

Partitioned into 247,451 symmetry classes.

Abstract

Flip-graph connectedness is established here for the vertex set of the 4-dimensional cube. It is found as a consequence that this vertex set has 92 487 256 triangulations, partitioned into 247 451 symmetry classes.