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Tessellations of the Euclidean, Elliptic and Hyperbolic Plane
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| Organization: | University of Potsdam |
| Department: | Institute of Physics |
| Organization: | University of Belgrade |
| Department: | Faculty of Mathematics |
| Organization: | Faculty of Mathematics, Belgrade |
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0212-296
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2003-03-24
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Tess is a package for generation and drawing of Archimedean (including regular and uniform) tessellations in Euclidean (E2), Elliptic (S2 - polyhedra), and Lobachevskian (L2, or hyperbolic) plane. The tiles of Archimedean tessellations are regular polygons and all vertices are of the same type. Tessellations are given with their vertex configuration. The vertex configuration does not define uniquely tiling, and the program calculates, for a given vertex configuration, all different (if any) realizations of the tiling. The package correctly finds all uniform (semi-regular) tilings, Archimedean tilings which are not uniform, and also `colored' realizations. A typical command for drawing a tiling is TessShow[{4,4,4,6}]. Beside the drawing of tessellations, the program provides additional data, such as: geometry and type of tessellation, number of possible realizations, angles of tiles and transformation rules between neighboring vertices. The drawing in hyperbolic plane is realized using the I. Knezevic, R. Sazdanovic & S. Vukmirovic package L2Primitives.
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Tessellation, Tiling, Hyperbolic plane, Lobachevskian plane, Polyhedra, Elliptic plane
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| L2Primitives.m (12.1 KB) - Mathematica Package | | Tess.m (57.5 KB) - Mathematica package (code) | | TessUsage.nb (114.5 KB) - Mathematica notebook (usage) |
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