Variations on the Three-Sphere: Laves' Labyrinth Lopped
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915937169440768 |
|---|---|
| author | Niu, Lauren Kamien, Randall D. |
| author_facet | Niu, Lauren Kamien, Randall D. |
| contents | 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 $\mathbb{R}^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12971 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Variations on the Three-Sphere: Laves' Labyrinth Lopped Niu, Lauren Kamien, Randall D. Soft Condensed Matter Mathematical Physics Metric Geometry 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 $\mathbb{R}^3$. |
| title | Variations on the Three-Sphere: Laves' Labyrinth Lopped |
| topic | Soft Condensed Matter Mathematical Physics Metric Geometry |
| url | https://arxiv.org/abs/2604.12971 |