Locally and Globally Regular Toroids with Less than 16 Hexagonal Faces

Lajos Szilassi
Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (2010)
Pages 511–512


In 2008, we presented three classes of equivelar toroids. We have shown examples of al combinatorial types of toroids for face number F ≤ 12. The data which uniquely determine these polyhedra are described in [2]. As a continuation of [1], here we show further examples for all combinatorial types of toroids with F ≤ 15. These constructions represent outstanding mathematical achievements, and they also have significance in the art as sculptures having pleasant visual appearance. Such sculptures will be shown at the exhibition of the conference.