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arXiv · 2604.12971

Variations on the Three-Sphere: Laves' Labyrinth Lopped

Lauren Niu·Randall D. Kamien
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Abstract

Inspired by the structure of $srs$ Laves networks in $\mathbb{R}^3$ that underpin the celebrated gyroid surface, we construct a Laves network of identical three-coordinated vertices on $S^3$ with 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 $S^3$, and describe their relation to the well-known $srs$ Laves network structure in $\mathbb{R}^3$.

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Lauren Niu, Randall D. Kamien. 2026-04-14. Variations on the Three-Sphere: Laves' Labyrinth Lopped. https://doi.org/10.1098/rsfs.2026.0021

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