Regular polyhedra in the 3-torus

2016/04/21 by Montero, Antonio
#Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1604.06499

Abstract

In this paper we discuss the classification rank 3 lattices preserved by finite orthogonal groups of isometries and derive from it the classification of regular polyhedra in the 3-dimensional torus. This classification is highly related to the classification of regular polyhedra in the 3-space.

Related

• Regular Polyhedra of Index Two, I
• Regular Polyhedra of Index Two, II
• Regular Polygonal Complexes in Space, I
• Polygonal Complexes and Graphs for Crystallographic Groups
• A complete isometry classification of 3-dimensional lattices