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Tessellations of the Euclidean, Elliptic and Hyperbolic Plane

Miodrag Sremcevic
Organization: University of Potsdam
Department: Institute of Physics
Radmila Sazdanovic
Organization: University of Belgrade
Department: Faculty of Mathematics
Srdjan Vukmirovic
Organization: Faculty of Mathematics, Belgrade
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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.

*Mathematics > Geometry > Plane Geometry
*Mathematics > Geometry > Tiling

Tessellation, Tiling, Hyperbolic plane, Lobachevskian plane, Polyhedra, Elliptic plane
Related items

*Basic drawing in the Hyperbolic plane   [in MathSource: Packages and Programs]
*L2Coordinates-Various Coordinates in the Hyperbolic Plane   [in MathSource: Packages and Programs]
Downloads Download Wolfram CDF Player

L2Primitives.m (12.1 KB) - Mathematica Package
Tess.m (57.5 KB) - Mathematica package (code)
TessUsage.nb (114.5 KB) - Mathematica notebook (usage)