Twofold orthogonal weavings on cuboids | Zendy

Flórián Kovács | Zendy

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Twofold orthogonal weavings on cuboids

Author(s) -

Flórián Kovács

Publication year - 2016

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2015.0576

Subject(s) - cuboid , polyhedron , tetrahedron , mathematics , connection (principal bundle) , geometry , plane (geometry) , combinatorics , pure mathematics

Some closed polyhedral surfaces can be completely covered by two-way, twofold (rectangular) weaving of strands of constant width. In this paper, a construction for producing all possible geometries for such weavable cuboids is proposed: a theorem on spherical octahedra is proven first that all further theory is based on. The construction method of weavable cuboids itself relies on successive truncations of an initial tetrahedron and is also extended for cases of degenerate (unbounded) polyhedra. Arguments are mainly based on the plane geometry of the development of the respective polyhedra, in connection with some of three-dimensional projective properties of the same.

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