---
title: Vertex-Unfoldings of Simplicial Manifolds
url: https://www.emergentmind.com/papers/0110054
type: paper
arxiv_id: '0110054'
arxiv_url: https://arxiv.org/abs/0110054
published: '2001-10-27'
categories:
- cs.CG
- cs.DM
---

# Vertex-Unfoldings of Simplicial Manifolds

## Abstract

We present an algorithm to unfold any triangulated 2-manifold (in particular, any simplicial polyhedron) into a non-overlapping, connected planar layout in linear time. The manifold is cut only along its edges. The resulting layout is connected, but it may have a disconnected interior; the triangles are connected at vertices, but not necessarily joined along edges. We extend our algorithm to establish a similar result for simplicial manifolds of arbitrary dimension.