2024/03/19 by Manuel Estevez, Érika Roldán, Estevez, Manuel +3
Mathematics · #0501 #0506 #05A99 #05B25 #05C10 #05C35 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #History and Overview (math.HO) #History and Theory of Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2403.12825
openalex publication_date 2024/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℝ3 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.