Nested polytopes with non-crystallographic symmetry induced by projection

Briony Thomas, Reidun Twarock, Motiejus Valiunas and Emilio Zappa
Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture (2015)
Pages 167–174


Inspired by the structures of viruses and fullerenes in biology and chemistry, we have recently developed a method to construct nested polyhedra and, more generally, nested polytopes in multi-dimensional geometry with non-crystallographic symmetry. In this paper we review these results, presenting them from a geometrical point of view. Examples and applications in science and design are discussed.