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- W2155682960 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." @default.
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- W2155682960 date "2012-04-18" @default.
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- W2155682960 title "Wrapping the cube and other polyhedra" @default.
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- W2155682960 doi "https://doi.org/10.1098/rspa.2012.0116" @default.
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