منابع مشابه
3D Well-composed Polyhedral Complexes
A binary three-dimensional (3D) image I is well-composed if the boundary surface of its continuous analog is a 2D manifold. In this paper, we present a method to locally “repair” the cubical complex Q(I) (embedded in R3) associated to I to obtain a polyhedral complex P (I) homotopy equivalent to Q(I) such that the boundary surface of P (I) is a 2D manifold (and, hence, P (I) is a well-composed ...
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A subdivided polyhedron is the graph obtained by adding vertices on some of the edges of the 1-skeleton of a polyhedron. We also consider subdivided polyhedral complexes, which are collections of polyhedra connected into a topological complex along faces (as in a beehive). We use these graphs to define abstract molecules, by placing atoms at the vertices and bonds along the edges. One of the si...
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We investigate the asymptotics of the number of “overlattices” of a cocompact lattice Γ in Aut(X), where X is a locally finite polyhedral complex. We use complexes of groups to prove an upper bound for general X, and a lower bound for certain right-angled buildings.
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We explore which polyhedra and polyhedral complexes can be formed by folding up a planar polygonal region and fastening it with one zipper. We call the reverse process a zipper unfolding. A zipper unfolding of a polyhedron is a path cut that unfolds the polyhedron to a planar polygon; in the case of edge cuts, these are Hamiltonian unfoldings as introduced by Shephard in 1975. We show that all ...
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We discuss two problems in combinatorial geometry. First, given a geometric polyhedral complex in R (a family of 3-polytopes attached face-to-face), can it always be realized over Q? We give a negative answer to this question, by presenting an irrational polyhedral complex with 1278 convex polyhedra. We then present a universality theorem on the space of realizations of such complexes. Second, ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2012
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2012-11194-3