Seeing the variety in tessellation artworks it’s natural to wonder about their underlying structure.
We might notice for example that tiles in different artworks have different amounts of rotation,
or a different number of neighboring tiles,
or that sometimes tiles are flipped.
In fact, 35 different tessellation symmetries underlie the artworks on this site — all with these properties:
A single tile shape, forming a recognizable figure
Translational symmetry — you can slide the entire pattern in a straight line and end up with an identical pattern
All tile edges are shapeable — no edge needs to be straight because the adjacent tile is a mirror image
(Mathematicians use the term isohedral for a tessellation with properties 1 and 2 — one tile shape, and translational symmetry.)
To understand the symmetries behind the artworks, please see these pages:
Tutorial - How artistic tessellations work, step-by-step
Diagrams & Art - A page for each symmetry, with a live diagram and example artworks