Kovács, Flórián (2015) Twofold orthogonal weavings on cuboids. PROCEEDINGS OF THE ROYAL SOCIETY A: MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES . (Submitted)
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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 3D projective properties of the same.
| Item Type: | Article |
|---|---|
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria T Technology / alkalmazott, műszaki tudományok > TA Engineering (General). Civil engineering (General) / általános mérnöki tudományok |
| Depositing User: | Flórián Kovács |
| Date Deposited: | 27 Sep 2015 22:47 |
| Last Modified: | 27 Sep 2015 22:47 |
| URI: | http://real.mtak.hu/id/eprint/28612 |
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