I first encountered tessellations while representing my school's maths department at an open day, we invited visitors to slide coloured plastic shapes into a shallow board with low borders that held each piece in place, and once they filled the board with no overlaps and no gaps, the beauty of tessellations spoke for itself.
Some patterns do more than just appear, they repeat, interlock, and cover space with perfect precision, they pack honey, armour snake skin with overlapping scales, tile your kitchen floor, and streamline warehouse shelves.
This blog post explores what tessellations are, how they work, and why they matter across design, science, and business.
A tessellation is a way of covering a flat surface with one or more shapes, called tiles, so that there are no gaps or overlaps. Think of it as a perfectly fitting jigsaw puzzle.
Regular Tessellations These are made by repeating just one kind of regular polygon (a shape with equal sides and angles). But here’s the catch: only three polygons can do this perfectly equilateral triangles, squares, and regular hexagons. Why? Because their interior angles fit together evenly around a point (360 degrees).
Imagine squares tiled like your kitchen floor. Four squares meet at each corner, with 90 degrees each, perfectly filling the space.
Semi-Regular Tessellations These combine two or more types of regular polygons, arranged so the pattern repeats and the same shapes meet at each vertex.
For example, a pattern that alternates squares and octagons creates an eye-catching, regular design that still fits perfectly.
Here's a geometric giggle :)
Why are regular tessellations impossible to have a conversation with?
¡sǝʌlǝsɯǝɥʇ ʇɐǝdǝɹ sʎɐʍlɐ ʎǝɥʇ ǝsnɐɔǝq
¡sǝʌlǝsɯǝɥʇ ʇɐǝdǝɹ sʎɐʍlɐ ʎǝɥʇ ǝsnɐɔǝq