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A tiling whose features are repeated regularly over a plane and which is constructed from only one tile fitted to itself in a number of different orientations is said to be isohedral. Good examples can be found in Islamic tiling patterns and the so-called regular division drawings of M C Escher. In spite of there being an innumerable number of tile shapes which can form such tilings, by no means all tiles can do so. Here we show how appropriate tile shapes can be characterised and generated.
The tutorial explains the concepts involved in some detail. It shows how all appropriate tiles can be generated from 93 different templates, which take the form of triangles, quadrilaterals, pentagons, or hexagons, and which can be accessed on different pages. From there, details of the isohedral tiling which can be formed by tiles from each template and an example of one such tiling can be found.
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