English

Spiral Unfoldings of Convex Polyhedra

Computational Geometry 2015-10-20 v2 Discrete Mathematics

Abstract

The notion of a spiral unfolding of a convex polyhedron, resulting by flattening a special type of Hamiltonian cut-path, is explored. The Platonic and Archimedian solids all have nonoverlapping spiral unfoldings, although among generic polyhedra, overlap is more the rule than the exception. The structure of spiral unfoldings is investigated, primarily by analyzing one particular class, the polyhedra of revolution.

Keywords

Cite

@article{arxiv.1509.00321,
  title  = {Spiral Unfoldings of Convex Polyhedra},
  author = {Joseph O'Rourke},
  journal= {arXiv preprint arXiv:1509.00321},
  year   = {2015}
}

Comments

22 pages, 36 figures, 4 references. Version 2 added a conjecture in a final section