A pattern of shapes that fit perfectly together!
A Tessellation (or Tiling) is when we cover a surface with a pattern of flat shapes so that there are no overlaps or gaps.
Octagons and Squares
A regular tessellation is a pattern made by repeating a regular polygon.
There are only 3 regular tessellations:
Look at a Vertex ...
For a regular tessellation, the pattern is identical at each vertex!
A semi-regular tessellation is made of two or more regular polygons. The pattern at each vertex must be the same!
There are only 8 semi-regular tessellations:
To name a tessellation, go around a vertex and write down how many sides each polygon has, in order ... like "3.12.12".
|And always start at the polygon with the least number of sides, so "3.12.12", not "12.3.12"|
|Question 1: For the tessellations above, is the pattern the same at each vertex?|
|Question 2: One of those patterns becomes different when we make a mirror-image of it ... which one?|
There are also "demiregular" tessellations, but mathematicians disagree on what they actually are!
And some people allow curved shapes (not just polygons) so we can have tessellations like these:
All these images were made using Tessellation Artist, with some color added using a paint program.
You can try it too - maybe you will invent a new tessellation!