Surfaces in The Tesseract
Geometric Topology
2023-11-14 v1 Combinatorics
History and Overview
Abstract
How can we visualize all the surfaces that can be made from the faces of the tesseract? In recent work, Aveni, Govc, and Rold\'an showed that the torus and the sphere are the only closed surfaces that can be realized by a subset of two-dimensional faces of the tesseract. They also gave an exhaustive list of all the isomorphic types of embeddings of these two surfaces. Here, we generate 3D models of all these surfaces. We also exhibit, with the help of some hyper-ants, the minimum realization of the M\"obius strip on the tesseract.
Keywords
Cite
@article{arxiv.2311.06596,
title = {Surfaces in The Tesseract},
author = {Manuel Estévez and Erika Roldan and Henry Segerman},
journal= {arXiv preprint arXiv:2311.06596},
year = {2023}
}
Comments
4 pages, 6 figures, Bridges 2023 Conference Proceedings