Tessellations
A tessellation (also called tiling) is when shapes are arranged side by side to produce a pattern with no gaps in between. Tessellations have existed since ancient Egyptian times and are still common today in floor and wall tilings. [Photo: pavement tessellation from wikipedia.com]
The simplist tessellations are the “regular tessellations” where only one shape is used. In order for the shapes to be flush one against another, the shape must be either a triangle, a square, or a hexagon. [Photo: the three possible types of regular tessellations from wikipedia.com].
Tessellations can be made with two or three shapes. These are called semiregular and demiregular tessellations. Tessellations can also be made with irregular shapes.
Most tessellations have a pattern that repeats itself over and over again but some tessellations, like the ones discovered by Robert Penrose do not repeat. These are called “aperiodic tessellations“.[Photo: an aperiodic tessellation from wikipedia.com].
Visit these sites for more information:
- Suzanne Alejandre and coolmath.com have good educational sites.
- make your own Escher-like tessellations at mathcats.com.
- David Annal’s site has a good tessellation database has a list of contemporary tessellations created by modern artists.
Origami Tessellations
can be regular (triangles, hexagons) or irregular (parallelograms, trapezoids). They are all periodic (repeating pattern).
- go to Origami Tessellations
- go to Origami Quilts
