Common Edge-Unzippings for Tetrahedra

TL;DR

This paper demonstrates that different tetrahedra with Hamiltonian edge paths can be unfolded into a shared net, revealing new insights into polyhedral edge-unzippings and their applications.

Contribution

It introduces the concept of common edge-unzippings for multiple tetrahedra, expanding understanding of polyhedral unfoldings and providing infinite classes of such examples.

Findings

Multiple distinct tetrahedra can share a common net when unfolded along Hamiltonian edge paths.

Infinite classes of tetrahedra with shared edge-unzippings are established.

Unfolding surfaces of these tetrahedra produce the same net, demonstrating a new property of polyhedral nets.

Abstract

It is shown that there are examples of distinct polyhedra, each with a Hamiltonian path of edges, which when cut, unfolds the surfaces to a common net. In particular, it is established for infinite classes of triples of tetrahedra.