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12.1 Tessellating shapes

12.1 Tessellating shapes

A tessellation is a pattern made of identical shapes. You can make your own tessellation by !tting copies
of a shape together, without gaps or overlaps. You say that the shape tessellates, or is a tessellating shape.

Here are some examples of shapes that tessellate with themselves.

Here are some examples of shapes that do not tessellate with themselves. $ere are gaps between the shapes.

When you make a tessellation you can move the shape by translating, rotating or re#ecting it.
For example, here are some of the ways you can tessellate a rectangle.

Many tessellations are made by repeating a shape and using half-turn rotations of the same shape.

For example, this triangle and a half-turn rotation of the same triangle !t together

exactly to make a tessellation like this.

In any tessellation, the sum of the angles at the point where the vertices of the shapes meet is 360°.
Look closely at three of the tessellations above.

90° 90° 90° + 90° + 90° + 90° = 360°
90° 90°

90° 90° 90° + 90° + 180° = 360°
180°

95°
37° 48° 37° + 95° + 48° + 37° + 95° + 48° = 360°
48° 95° 37°

12 Tessellations, transformations and loci 111