This PREP workshop was made possible by the NSF grant DUE: 0341481

From Prep08Wiki

We spend quite a bit of time on tessellations.

• Tesselations by polygons: All triangles and quadrilaterals tessellate. The classification of which convex polygons tessellate is interesting and leads to still unsolved mathematical questions.
• Regular tessellations: We restrict our attention to those tessellations that are made up of regular polygons. It is possible to lead the students through a proof that there are exactly 3 regular tessellations of the plane. There is a little bit of hand waving, but the idea of a carefully crafted argument to show such a general statement is worth doing.
• Semi-regular tessellations: Using more than one type of regular polygon but with some condition on the vertex configuration is a nice exerxise.
• Regular and semi-regular tessellations can (and maybe should) be revisited when we do Spherical and Hyperbolic geometry. In those geometries the number of possibilities for each of the different types of tessellations is different.

See

• escherwiki:Tessellation Exploration: The Basics
• escherwiki:Angles of Polygons and Regular Tessellations Exploration
• escherwiki:Escher-Like Tessellations Explorations