Journal
PLOS ONE
Volume 16, Issue 6, Pages -Publisher
PUBLIC LIBRARY SCIENCE
DOI: 10.1371/journal.pone.0252613
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Funding
- Australian Research Council [DE170101062]
- Australian Research Council [DE170101062] Funding Source: Australian Research Council
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The study developed a path-planning algorithm based on the breadth-first-search algorithm to generate a shortest path for each Platonic solid to reach a desired pose. In addition, the authors chose Penrose tiling as the method for regular-pentagon tiling.
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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