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 rollingcube puzzles for a cubic dice. We developed...
| Main Authors: | , , |
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| Format: | Journal Article |
| Language: | English |
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PUBLIC LIBRARY SCIENCE
2021
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| Subjects: | |
| Online Access: | http://purl.org/au-research/grants/arc/DE170101062 http://hdl.handle.net/20.500.11937/90117 |
| _version_ | 1848765329790992384 |
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| author | Lam, Ngoc Tam Howard, Ian Cui, Lei |
| author_facet | Lam, Ngoc Tam Howard, Ian Cui, Lei |
| author_sort | Lam, Ngoc Tam |
| building | Curtin Institutional Repository |
| collection | Online Access |
| 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 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. |
| first_indexed | 2025-11-14T11:33:32Z |
| format | Journal Article |
| id | curtin-20.500.11937-90117 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T11:33:32Z |
| publishDate | 2021 |
| publisher | PUBLIC LIBRARY SCIENCE |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-901172023-02-13T05:23:54Z Path planning for the Platonic solids on prescribed grids by edge-rolling Lam, Ngoc Tam Howard, Ian Cui, Lei Science & Technology Multidisciplinary Sciences Science & Technology - Other Topics 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. 2021 Journal Article http://hdl.handle.net/20.500.11937/90117 10.1371/journal.pone.0252613 English http://purl.org/au-research/grants/arc/DE170101062 http://creativecommons.org/licenses/by/4.0/ PUBLIC LIBRARY SCIENCE fulltext |
| spellingShingle | Science & Technology Multidisciplinary Sciences Science & Technology - Other Topics Lam, Ngoc Tam Howard, Ian Cui, Lei Path planning for the Platonic solids on prescribed grids by edge-rolling |
| title | 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_short | 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 |
| topic | Science & Technology Multidisciplinary Sciences Science & Technology - Other Topics |
| url | http://purl.org/au-research/grants/arc/DE170101062 http://hdl.handle.net/20.500.11937/90117 |