CUED Publications database

Wrapping the cube and other polyhedra

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

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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
Uncontrolled Keywords: Polyhedra Weaving Wrapping
Subjects: UNSPECIFIED
Divisions: Div D > Structures
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 11:44
Last Modified: 08 Dec 2014 02:38
DOI: 10.1098/rspa.2012.0116