Vertex-Unfoldings of Simplicial Polyhedra

TL;DR

This paper introduces two algorithms for unfolding any triangulated polyhedron's surface into a nonoverlapping planar layout, cutting only along edges, with a connected layout but possibly disconnected interior.

Contribution

It presents novel algorithms for vertex-unfolding triangulated polyhedra, ensuring a connected layout with minimal cuts along edges.

Findings

Algorithms successfully produce nonoverlapping layouts

Layouts are connected but may have disconnected interiors

Applicable to all polyhedra with triangular faces

Abstract

We present two algorithms for unfolding the surface of any polyhedron, all of whose faces are triangles, to a nonoverlapping, connected planar layout. The surface is cut only along polyhedron edges. The layout is connected, but it may have a disconnected interior: the triangles are connected at vertices, but not necessarily joined along edges.