---
title: Vertex-Unfoldings of Simplicial Polyhedra
url: https://www.emergentmind.com/papers/0107023
type: paper
arxiv_id: '0107023'
arxiv_url: https://arxiv.org/abs/0107023
published: '2001-07-18'
categories:
- cs.CG
- cs.DM
---

# Vertex-Unfoldings of Simplicial Polyhedra

## 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.