12.6. Extension: Tessellations http://www.ck12.org
12.6 Extension: Tessellations
Learning Objectives
- Determine whether or not a given shape will tessellate.
- Draw your own tessellation.
What is a Tessellation?
You have probably seen tessellations before, even though you did not call them that. Examples of a tessellation are:
a tile floor, a brick or block wall, a checker or chess board, and a fabric pattern.
Tessellation:A tiling over a plane with one or more figures such that the figures fill the plane with no overlaps and
no gaps.
Here are a few examples.
Notice the hexagon (cubes, first tessellation) and the quadrilaterals fit together perfectly. If we keep adding more,
they will entirely cover the plane with no gaps or overlaps. The tessellation pattern could be colored creatively to
make interesting and/or attractive patterns.
To tessellate a shape it must be able to exactly surround a point, or the sum of the angles around each point in a
tessellation must be 360◦. Therefore, every quadrilateral and hexagon will tessellate.
Example 1:Tessellate the quadrilateral below.
Solution:To tessellate any image you will need to reflect and rotate the image so that the sides all fit together. First,
start by matching up each side with itself around the quadrilateral.