Surfaces in the Tesseract
Manuel Estévez, Érika Roldán, and Henry Segerman

Proceedings of Bridges 2023: Mathematics, Art, Music, Architecture, Culture
Pages 441–444
Short Papers

Abstract

How can we visualize all the surfaces that can be made from the faces of the tesseract? In recent work, Aveni, Govc, and Roldán showed that the 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 embedings 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 Möbius strip on the tesseract.

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