منابع مشابه
Vertex-Unfoldings of Simplicial Polyhedra
We present two algorithms for unfolding the surface of any polyhedron, all of whose faces are triangles, to a nonoverlapping, connected planar layout. The surface is cut only along polyhedron edges. The layout is connected, but it may have a disconnected interior: the triangles are connected at vertices, but not necessarily joined along edges.
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An unfolding of a polyhedron along its edges is called a vertex unfolding if adjacent faces are allowed to be connected at not only an edge but also a vertex. Demaine et al [1] showed that every triangulated polyhedron has a vertex unfolding. We extend this result to a tight polyhedron, where a polyhedron is tight if its non-triangular faces are mutually non-incident.
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An edge-unfolding of a polyhedron is produced by cutting along edges and flattening the faces to a net, a connected planar piece with no overlaps. A grid unfolding allows additional cuts along grid edges induced by coordinate planes passing through every vertex. A vertexunfolding permits faces in the net to be connected at single vertices, not necessarily along edges. We show that any orthogona...
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We introduce a new notion that connects the combinatorial concept of regularity with the geometrical notion of face transitivity. This new notion implies finiteness results in the case of bounded maximal face size. We give lists of structures for some classes and investigate polyhedra with constant vertex degrees and faces of only two sizes.
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Consider all geodesics between two given points on a polyhedron. On the regular tetrahedron, we describe all the geodesics from a vertex to a point, which could be another vertex. Using the Stern– Brocot tree to explore the recursive structure of geodesics between vertices on a cube, we prove, in some precise sense, that there are twice as many geodesics between certain pairs of vertices than o...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2020
ISSN: 0012-365X
DOI: 10.1016/j.disc.2020.112013