Let’s go through some regular polygons one by one to see why only three work and the others don’t.
Remember, the sum of the interior angles of a regular polygon is
(n - 2) x 180° where n is the number of sides of the polygon. The interior angle at any vertex of a regular polygon is
(n - 2) x 180° .
n
REGULAR TESSELLATIONS are made up entirely of identically sized and shaped regular polygons.
Every vertex looks the same and the sum of the interior angles at each vertex is 360°.
Only three combinations of singular regular polygons create regular tessellations.
Now that we have a better understanding of some basic geometry, let’s move onto the classification of tessellations of which there are three: regular, semi-regular and non-regular.