Intricate Isohedral Tilings of 3D Euclidean Space

Carlo H. Séquin
Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture (2008)
Pages 139–148


Various methods to create intricate tilings of 3D space are presented. They include modulated extrusions of 2D Escher tilings, free-form deformations of the fundamental domain of various 3D symmetry groups, highly symmetrical polyhedral toroids of genus 1, higher-genus cage structures derived from the cubic lattice as well as from the diamond and triamond lattices, and finally interlinked tiles with the connectivity of simple knots.