Modular Toroids Constructed from Nonahedra
Yifat Amir and Carlo H. Séquin

Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture
Pages 131–138
Regular Papers

Abstract

Inspired by a piece of artwork by Bente Simonsen at Bridges 2016, we explore various ways of making modular polyhedral toroids from the same basic nonahedron building block. Since the chosen building block cannot be an ideal, regular Johnson solid, we use greedy optimization methods, such as gradient descent, to minimize the deviations from regular n-gons for the facets of the nonahedron, while maintaining the planarity of the connecting faces for each respective toroidal configuration. In general, we formulate our objective to maximize overall symmetry and create a visually aesthetic result. Furthermore, we have constructed polyhedra with a genus as high as 11 using a 3D printer.

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