Optimizing for the Rupert property
Optimization and Control
2023-10-09 v2 Combinatorics
Metric Geometry
Abstract
A polyhedron is Rupert if it is possible to cut a hole in it and thread an identical polyhedron through the hole. It is known that all 5 Platonic solids, 10 of the 13 Archimedean solids, 9 of the 13 Catalan solids, and 82 of the 92 Johnson solids are Rupert. Here, a nonlinear optimization method is devised that is able to validate the previously known results in seconds. It is also used to show that 2 additional Catalan solids -- the triakis tetrahedron and the pentagonal icositetrahedron -- and 5 additional Johnson solids are Rupert.
Cite
@article{arxiv.2210.00601,
title = {Optimizing for the Rupert property},
author = {Albin Fredriksson},
journal= {arXiv preprint arXiv:2210.00601},
year = {2023}
}