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: | , , |
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| Formato: | article |
| Lenguaje: | EN |
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Public Library of Science (PLoS)
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/78ee25d7238d406a9e3beebc275c070e |
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| Sumario: | 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. |
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