Covering polyhedra by motifs with triangular fundamental regions.

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Covering polyhedra by motifs with triangular fundamental regions.

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2011-09

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In geometry, a “net” of a polyhedron is a two-dimensional figure where all the polygons are joined by edges, which when folded becomes a three-dimensional polyhedron. A “subnet” is a subset of a net which is formed by the faces of the polyhedron. Technically, multiple nets can exist for a polyhedron and different polyhedrons can be obtained from a single net. The algorithm designed takes any arbitrary subnet of a polyhedron as an input and maps a triangular motif onto each of the polygon faces of the subnet. Each polygon face is assumed to be convex and will be triangulated from its centroid. The triangles of that triangulation will then be filled in with transformed versions of the motif. Currently, Dr Dunham's work creates a pattern on a specific polyhedron while my research aims at mapping a single pattern onto each of the possibly different polygons of a net that can be used to construct any patterned polyhedron.

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University of Minnesota M.S. thesis. September 2011. Major: Computer science. Advisor:Dr. Douglas Dunham. 1 computer file (PDF); vi, 37 pages. appendix p. 35-37.

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Pathi, Lakshmi Ramya. (2011). Covering polyhedra by motifs with triangular fundamental regions.. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/117011.

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