Tarnai, T and Kovács, F and Fowler, PW and Guest, SD (2012) *Wrapping the cube and other polyhedra.* Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468. pp. 2652-2666. ISSN 1364-5021

## Abstract

An infinite series of twofold, two-way weavings of the cube, corresponding to 'wrappings', or double covers of the cube, is described with the aid of the two-parameter Goldberg- Coxeter construction. The strands of all such wrappings correspond to the central circuits (CCs) of octahedrites (four-regular polyhedral graphs with square and triangular faces), which for the cube necessarily have octahedral symmetry. Removing the symmetry constraint leads to wrappings of other eight-vertex convex polyhedra. Moreover, wrappings of convex polyhedra with fewer vertices can be generated by generalizing from octahedrites to i-hedrites, which additionally include digonal faces. When the strands of a wrapping correspond to the CCs of a four-regular graph that includes faces of size greater than 4, non-convex 'crinkled' wrappings are generated. The various generalizations have implications for activities as diverse as the construction of woven-closed baskets and the manufacture of advanced composite components of complex geometry. © 2012 The Royal Society.

Item Type: | Article |
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Uncontrolled Keywords: | Polyhedra Weaving Wrapping |

Subjects: | UNSPECIFIED |

Divisions: | Div D > Structures |

Depositing User: | Cron job |

Date Deposited: | 16 Jul 2015 13:46 |

Last Modified: | 10 Oct 2015 02:59 |

DOI: | 10.1098/rspa.2012.0116 |