Path planning for the Platonic solids on prescribed grids by edge-rolling.

The five Platonic solids-tetrahedron, cube, octahedron, dodecahedron, and icosahedron-have found many applications in mathematics, science, and art. Path planning for the Platonic solids had been suggested, but not validated, except for solving the rolling-cube puzzles for a cubic dice. We developed...

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Autores principales:	Ngoc Tam Lam, Ian Howard, Lei Cui
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/78ee25d7238d406a9e3beebc275c070e
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id	oai:doaj.org-article:78ee25d7238d406a9e3beebc275c070e
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spelling	oai:doaj.org-article:78ee25d7238d406a9e3beebc275c070e2021-12-02T20:11:08ZPath planning for the Platonic solids on prescribed grids by edge-rolling.1932-620310.1371/journal.pone.0252613https://doaj.org/article/78ee25d7238d406a9e3beebc275c070e2021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0252613https://doaj.org/toc/1932-6203The five Platonic solids-tetrahedron, cube, octahedron, dodecahedron, and icosahedron-have found many applications in mathematics, science, and art. Path planning for the Platonic solids had been suggested, but not validated, except for solving the rolling-cube puzzles for a cubic dice. We developed a path-planning algorithm based on the breadth-first-search algorithm that generates a shortest path for each Platonic solid to reach a desired pose, including position and orientation, from an initial one on prescribed grids by edge-rolling. While it is straightforward to generate triangular and square grids, various methods exist for regular-pentagon tiling. We chose the Penrose tiling because it has five-fold symmetry. We discovered that a tetrahedron could achieve only one orientation for a particular position.Ngoc Tam LamIan HowardLei CuiPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 6, p e0252613 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Ngoc Tam Lam Ian Howard Lei Cui Path planning for the Platonic solids on prescribed grids by edge-rolling.
description	The five Platonic solids-tetrahedron, cube, octahedron, dodecahedron, and icosahedron-have found many applications in mathematics, science, and art. Path planning for the Platonic solids had been suggested, but not validated, except for solving the rolling-cube puzzles for a cubic dice. We developed a path-planning algorithm based on the breadth-first-search algorithm that generates a shortest path for each Platonic solid to reach a desired pose, including position and orientation, from an initial one on prescribed grids by edge-rolling. While it is straightforward to generate triangular and square grids, various methods exist for regular-pentagon tiling. We chose the Penrose tiling because it has five-fold symmetry. We discovered that a tetrahedron could achieve only one orientation for a particular position.
format	article
author	Ngoc Tam Lam Ian Howard Lei Cui
author_facet	Ngoc Tam Lam Ian Howard Lei Cui
author_sort	Ngoc Tam Lam
title	Path planning for the Platonic solids on prescribed grids by edge-rolling.
title_short	Path planning for the Platonic solids on prescribed grids by edge-rolling.
title_full	Path planning for the Platonic solids on prescribed grids by edge-rolling.
title_fullStr	Path planning for the Platonic solids on prescribed grids by edge-rolling.
title_full_unstemmed	Path planning for the Platonic solids on prescribed grids by edge-rolling.
title_sort	path planning for the platonic solids on prescribed grids by edge-rolling.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/78ee25d7238d406a9e3beebc275c070e
work_keys_str_mv	AT ngoctamlam pathplanningfortheplatonicsolidsonprescribedgridsbyedgerolling AT ianhoward pathplanningfortheplatonicsolidsonprescribedgridsbyedgerolling AT leicui pathplanningfortheplatonicsolidsonprescribedgridsbyedgerolling
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Path planning for the Platonic solids on prescribed grids by edge-rolling.

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