Tesselmania is a software program that allows you to create your own tesselations. To create the tessellations for you, the program uses three basic transformations: translations, rotations, and glide reflections.
To help you see how a quadrilateral, hexagon, or triangle is transformed, the program uses a labeling system invented by the German mathematician Heinrich Heesch called Heesch Type. The system consists of moving around the sides of the initial tile clockwise. Each side is labeled by one of the following, according to how it was transformed...
Notice that some of the letters have subscripts. These are used to help better organize the transformations. The "T" 's, or translations, will never have subscripts because the translation must always be to the opposite side. The subscripts on the "C" 's, or rotations, will tell you how many fold, or the number of degrees it was rotated (when talking about the "folds", think of how many pieces you get when folding a piece of paper that many times).
The subscripts on the "G" 's, or glide reflections, help to distinguish between the pairs of glide reflections, since the glide reflections can use either the adjacent or opposite side.
Heinrich Heesch invented 28 different types "of asymmetric tiles that can fill the plane in an isohedral manner without using reflections" [Schattschneider, Visions of Symmetry, 1990, 326]. Tesselmania only uses 15 of the 28 types. There are eleven based on quadrilaterals, two based on hexagons, and two based on triangles.
The software program Tesselmania! is recommended for children in Grades 3 and up. To download a demo of Tesselmania! or to buy the software click HERE to visit The World of Escher. (All of the above information was found in the Tesselmania! Demo.)
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