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Twofold orthogonal weavings on cuboids.

ABSTRACT: 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.

SUBMITTER: Kovacs F

PROVIDER: S-EPMC4841476 | biostudies-literature | 2016 Mar

REPOSITORIES: biostudies-literature

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Twofold orthogonal weavings on cuboids.

Kovács Flórián F

Proceedings. Mathematical, physical, and engineering sciences 20160301 2187

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. ...[more]

PMID: 27118910

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