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Surfaces in The Tesseract

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arxiv 2311.06596 v1 pith:QWE4ERBQ submitted 2023-11-11 math.GT math.COmath.HO

Manuel Estévez , Erika Roldan , Henry Segerman This is my paper · ORCID
classification math.GTmath.COmath.HO
keywords surfacestesseractfacesaveniclosedembeddingsexhaustiveexhibit
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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.

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