Objectives
To identify figures that tessellate
To identify transformations and symmetries in tessellations
A tessellation, or tiling, is a repeating pattern of figures that completely covers a plane, without gaps or overlaps. You can make tessellations with translations, rotations, and reflections. You can find shapes that tessellate in art (see Problem 1 below), nature (cells in a honeycomb), and everyday life (tiled floors).
Essential Understanding Some shapes can fit together in a repeating pattern that fills a plane without gaps or overlaps. The angle measures of polygons that fit together in this way have a special relationship.
Art What is the repeating figure in this tessellation? What transformation does the tessellation use?
How do you recognize the transformation?
Comparing the positions of several pairs of corresponding points will help you see how the points moved.
This tessellation uses a rotation. The fish, bird, and two turtles together form the repeating figure. The arrows show how each point of the repeating figure rotates.