Triply Periodic Helical Weaves

Fuente: arXiv

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Detalles Bibliográficos
Autores principales:	Wetzel, Duston, Gailiunas, Paul, Gaither-Ganim, Moses, Holt, William
Formato:	Preprint
Publicado:	2024
Materias:	Geometric Topology
Acceso en línea:	Acceder al recurso
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author	Wetzel, Duston Gailiunas, Paul Gaither-Ganim, Moses Holt, William
author_facet	Wetzel, Duston Gailiunas, Paul Gaither-Ganim, Moses Holt, William
contents	Weaving typically involves forming a sufrace by interlacing fibers into a mechanically stable arrangement, effectively making a two-dimensional object out of one-dimensional objects. Moorish Fretwork involves interweaving solid helical elements into mechanically stable two-dimensional arrangements by exploiting the helices' screw symmetry. A three-dimensional extension of this idea was demonstrated by Alexandru Usineviciu at Bridges in 2015. Here we expand the idea further by considering cases informed by invariant cylindrical rod packing, and cases related to geodesics of the gyroid. Simulations and/or physical models of nineteen triply periodic arrangements of interwoven helices are shown, with physical models demonstrated for eight.
format	Preprint
id	arxiv_https___arxiv_org_abs_2402_07849
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Triply Periodic Helical Weaves Wetzel, Duston Gailiunas, Paul Gaither-Ganim, Moses Holt, William Geometric Topology Weaving typically involves forming a sufrace by interlacing fibers into a mechanically stable arrangement, effectively making a two-dimensional object out of one-dimensional objects. Moorish Fretwork involves interweaving solid helical elements into mechanically stable two-dimensional arrangements by exploiting the helices' screw symmetry. A three-dimensional extension of this idea was demonstrated by Alexandru Usineviciu at Bridges in 2015. Here we expand the idea further by considering cases informed by invariant cylindrical rod packing, and cases related to geodesics of the gyroid. Simulations and/or physical models of nineteen triply periodic arrangements of interwoven helices are shown, with physical models demonstrated for eight.
title	Triply Periodic Helical Weaves
topic	Geometric Topology
url	https://arxiv.org/abs/2402.07849

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