Variations on the three-sphere: Laves' labyrinth lopped

Abstract

Abstract Inspired by the structure of srs Laves networks in R3 that underpin the celebrated gyroid surface, we construct a Laves network of identical three-coordinated vertices on S3 with a double twist. This network is a subset of the vertices and edges of the 600-cell, and can be viewed as a bipartite graph of disjoint 24-cell vertices inscribed in the 600-cell. We describe mutually entangled realizations of this network on S3 and describe their relation to the well-known srs Laves network structure in R3. This article is part of the theme issue ‘Geometry, materials and the imagination’.