# TESSELMANIA!

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...

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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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AND ESCHER