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The number of corner polyhedra graphs
Published 2020-04-01“…Corner polyhedra were introduced by Eppstein and Mumford (2014) as the set of simply connected 3D polyhedra such that all vertices have non negative integer coordinates, edges are parallel to the coordinate axes and all vertices but one can be seen from infinity in the direction (1, 1, 1). …”
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The Roundest Polyhedra with Symmetry Constraints
Published 2017-03-01Subjects: “…polyhedra…”
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Formalizing the Face Lattice of Polyhedra
Published 2022-05-01“…Faces play a central role in the combinatorial and computational aspects of polyhedra. In this paper, we present the first formalization of faces of polyhedra in the proof assistant Coq. …”
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Heuristics of Regular Polyhedra For Research
Published 2012-07-01“…Platonic polyhedra are carriers of a high heuristic potential for new developments in the field of art, science and technology. …”
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Continuous Blooming of Convex Polyhedra
Published 2011“…We construct the first two continuous bloomings of all convex polyhedra. First, the source unfolding can be continuously bloomed. …”
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Refold rigidity of convex polyhedra
Published 2015“…If the unfolding is restricted to cut only edges of the polyhedron, we identify several polyhedra that are “edge-refold rigid” in the sense that each of their unfoldings may only fold back to the original. …”
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Geometric folding algorithms : linkages, origami, polyhedra /
Published 2007Subjects: “…Polyhedra…”
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UNFOLDED REGULAR AND SEMI-REGULAR POLYHEDRA
Published 2015-07-01“…This paper proposes a presentation unfolding regular and semi-regular polyhedra. Regular polyhedra are convex polyhedra whose faces are regular and equal polygons, with the same number of sides, and whose polyhedral angles are also regular and equal. …”
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UNFOLDED REGULAR AND SEMI-REGULAR POLYHEDRA
Published 2015-06-01“…This paper proposes a presentation unfolding regular and semi-regular polyhedra. Regular polyhedra are convex polyhedra whose faces are regular and equal polygons, with the same number of sides, and whose polyhedral angles are also regular and equal. …”
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Regular and Chiral Polyhedra in Euclidean Nets
Published 2016-10-01“…We enumerate the regular and chiral polyhedra (in the sense of Grünbaum’s skeletal approach) whose vertex and edge sets are a subset of those of the primitive cubic lattice, the face-centred cubic lattice, or the body-centred cubic lattice.…”
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UNFOLDED REGULAR AND SEMI-REGULAR POLYHEDRA
Published 2015-07-01“…This paper proposes a presentation unfolding regular and semi-regular polyhedra. Regular polyhedra are convex polyhedra whose faces are regular and equal polygons, with the same number of sides, and whose polyhedral angles are also regular and equal. …”
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