Playing with the Platonics: A New Class of Polyhedra

Walt van Ballegooijen
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 119–124

Abstract

Intrigued by the impossibility of making a closed loop of face-to-face connected regular tetrahedra, I wondered how adjustments to the polyhedron could make it loop-able. As a result I have defined a method to construct a whole class of new polyhedra based on the Platonic solids. By exploring this class I found several examples of polyhedra that do make closed loops possible, and sometimes it is possible to build 3D lattices or other regular 3D structures with them. This project was however not a complete analyses of all possibilities, but merely a short study.

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