تقرير
Oriented and Non-oriented Cubical Surfaces in The Penteract
| العنوان: | Oriented and Non-oriented Cubical Surfaces in The Penteract |
|---|---|
| المؤلفون: | Estevez, Manuel, Roldan, Erika, Segerman, Henry |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Geometric Topology, Mathematics - Combinatorics, Mathematics - History and Overview, 0501, 0506, 05A99, 05B25, 05C10, 05C35 |
| الوصف: | Which surfaces can be realized with two-dimensional faces of the five-dimensional cube (the penteract)? How can we visualize them? In recent work, Aveni, Govc, and Roldan, show that there exist 2690 connected closed cubical surfaces up to isomorphism in the 5-cube. They give a classification in terms of their genus $g$ for closed orientable cubical surfaces and their demigenus $k$ for a closed non-orientable cubical surface. In this paper, we explain the main idea behind the exhaustive search and we visualize the projection to $\mathbb{R}^3$ of a torus, a genus two torus, the projective plane, and the Klein bottle. We use reinforcement learning techniques to obtain configurations optimized for 3D printing. Comment: 5 pages, 3 Figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.12825 |
| رقم الأكسشن: | edsarx.2403.12825 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |