Have you ever wondered how beautiful mosaic tile designs are made? The tiles must cover a flat surface with shapes that fit together without any gaps. The lengths of the sides of the tile pieces must match up and the angles must be correct for this to work.

Polygons are simple closed figures with straight-line sides. Regular polygons are easy to tile since all sides and angles are the same size. Some examples of regular polygons are equilateral triangles (3 equal sides and 3 equal angles) and squares (4 equal sides and 4 equal angles).

Discuss within your group combinations of different regular polygons that you can tile. For example, three triangles and two squares can be used to surround one of the vertices of one of the triangles. A vertex is a point on the tilings where the corners of the polygons fit together shown in the diagram by the star. Use a piece of graph paper to display your combinations. Be prepared to share your combinations with the class.