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 |
| Summary: | 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. |
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