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Award ID contains: 2203993

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  1. ; ; (, Bridges Conference Proceedings)
    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 Roldán 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 present the definition of a cubical surface and we visualize the projection to $R^3$ 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. 
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    Accepted Manuscript Full Text Available
  2. ; (, Groups, Geometry, and Dynamics)
    We introduce loom spaces, a generalisation of both the leaf spaces associated to pseudo- Anosov flows and the link spaces associated to veering triangulations. Following work of Guéritaud, we prove that there is a locally veering triangulation canonically associated to every loom space, and that the realisation of this triangulation is homeomorphic to R^3. 
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    Full Text Available 
  3. ; ; (, Bridges 2023 Conference Proceedings)
    Holdener, Judy; Torrence, Eve; Fong, Chamberlain (Ed.)
    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 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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    Accepted Manuscript Full Text Available
  4. ; (, Proceedings of Bridges 2022: Mathematics, Art, Music, Architecture, Culture)
    Reimann, David; Norton, Douglas (Ed.)
    From a self-similar quadrilateral tiling, we construct a scissor grid by replacing each quadrilateral with a scissor linkage. We show that the resulting linkage is deployable if and only if the quadrilaterals are cyclic or parallelograms. 
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    Accepted Manuscript Full Text Available