Spidronised Space-Fillers

Walt van Ballegooijen, Paul Gailiunas and Dániel Erdély
Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture (2009)
Pages 271–278 Regular Papers


Saddle polyhedra have faces that are skew polygons, with edges that do not lie in one plane. The surface of a face can be undefined [1], a minimal surface [2], triangulated [3], or filled using a spidron nest [4,5]. Identifying circuits in three dimensional periodic networks of vertices and edges [6] with saddle faces generates space-filling saddle polyhedra, described in [2]. We consider these space-fillers, and by extending the concept of a spidron so it can be applied to the faces create forms that are visually interesting, both as individual polyhedra and in aggregations.