Towards a Geometric Understanding of the 4-Dimensional Point Groups
Metric Geometry
2022-05-11 v1
Abstract
We classify the finite groups of orthogonal transformations in 4-space, and we study these groups from the viewpoint of their geometric action, using polar orbit polytopes. For one type of groups (the toroidal groups), we develop a new classification based on their action on an invariant torus, while we rely on classic results for the remaining groups. As a tool, we develop a convenient parameterization of the oriented great circles on the 3-sphere, which leads to (oriented) Hopf fibrations in a natural way.
Keywords
Cite
@article{arxiv.2205.04965,
title = {Towards a Geometric Understanding of the 4-Dimensional Point Groups},
author = {Laith Rastanawi and Günter Rote},
journal= {arXiv preprint arXiv:2205.04965},
year = {2022}
}
Comments
109 pages, 56 figures, 18 tables