Regular polyhedra in the 3-torus
Antonio Montero

TL;DR
This paper classifies regular polyhedra in the 3-torus by analyzing rank 3 lattices preserved by finite orthogonal groups, linking it to the classification of regular polyhedra in 3-space.
Contribution
It provides a novel classification of regular polyhedra in the 3-torus based on lattice and symmetry group analysis, extending known classifications in 3-space.
Findings
Classification of rank 3 lattices preserved by finite orthogonal groups
Derivation of regular polyhedra in the 3-torus from lattice analysis
Connection established between 3-torus polyhedra and 3-space polyhedra
Abstract
In this paper we discuss the classification rank lattices preserved by finite orthogonal groups of isometries and derive from it the classification of regular polyhedra in the -dimensional torus. This classification is highly related to the classification of regular polyhedra in the -space.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · graph theory and CDMA systems · Advanced Algebra and Logic
