Factorization of Platonic Polytopes into canonical spheres

TL;DR

This paper explores how to decompose the skeleta of Platonic polytopes like the simplex, cube, and cross-polytope into canonical spheres, employing explicit methods and Keevash's design existence proof.

Contribution

It provides new methods for factorizing Platonic polytope skeleta into spheres, combining explicit constructions with advanced combinatorial existence proofs.

Findings

Successful factorization of simplex, cube, and cross-polytope skeleta into spheres.

Application of Keevash's design existence proof to polytope skeleta.

Explicit factorization methods demonstrated for specific Platonic polytopes.

Abstract

Factorization into spheres is achieved for skeleta of the simplex, cube, and cross-polytope, both explicitly and using Keevash's proof of existence of designs.