Path planning for the Platonic solids on prescribed grids by edge-rolling
dc.contributor.author | Lam, Ngoc Tam | |
dc.contributor.author | Howard, Ian | |
dc.contributor.author | Cui, Lei | |
dc.date.accessioned | 2023-01-24T05:49:24Z | |
dc.date.available | 2023-01-24T05:49:24Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Lam, N.T. and Howard, I. and Cui, L. 2021. Path planning for the Platonic solids on prescribed grids by edge-rolling. PLoS ONE. 16 (6 June): ARTN e0252613. | |
dc.identifier.uri | http://hdl.handle.net/20.500.11937/90117 | |
dc.identifier.doi | 10.1371/journal.pone.0252613 | |
dc.description.abstract |
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 rollingcube 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. | |
dc.language | English | |
dc.publisher | PUBLIC LIBRARY SCIENCE | |
dc.relation.sponsoredby | http://purl.org/au-research/grants/arc/DE170101062 | |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
dc.subject | Science & Technology | |
dc.subject | Multidisciplinary Sciences | |
dc.subject | Science & Technology - Other Topics | |
dc.title | Path planning for the Platonic solids on prescribed grids by edge-rolling | |
dc.type | Journal Article | |
dcterms.source.volume | 16 | |
dcterms.source.number | 6 June | |
dcterms.source.issn | 1932-6203 | |
dcterms.source.title | PLoS ONE | |
dc.date.updated | 2023-01-24T05:49:24Z | |
curtin.department | School of Civil and Mechanical Engineering | |
curtin.accessStatus | Open access | |
curtin.faculty | Faculty of Science and Engineering | |
curtin.contributor.orcid | Cui, Lei [0000-0003-2283-5079] | |
curtin.contributor.orcid | Howard, Ian [0000-0003-3999-9184] | |
curtin.contributor.orcid | Lam, Ngoc Tam [0000-0001-6478-5802] | |
curtin.identifier.article-number | ARTN e0252613 | |
dcterms.source.eissn | 1932-6203 | |
curtin.contributor.scopusauthorid | Cui, Lei [35168967600] | |
curtin.contributor.scopusauthorid | Howard, Ian [12808325800] |