The Tiling Atlas
Tiles1Configs2Library3Play4Theory5Parquet6Freedraw7Colors8

Theory

Background reading for the atlas: the mathematics behind the tilings, each with worked examples and interactive previews.

The eleven uniform tilings

The three regular and eight semiregular tilings of the plane, the angle equation that constrains them, and why there are exactly eleven.

Freedraw: the edges carry the tiling

Marek Čtrnáct's edge-subset construction: fix a grid, choose which edges are drawn, and let the tiles fall out. Planar grids and all five Platonic solids.

Islamic geometric patterns

The design systems behind Islamic star patterns: the tessellations underneath, with interactive previews of the curated tilings.

Why the hyperbolic catalogue stops where it does

The hyperbolic tilings never run out, so the enumeration is bounded by palette, valence and uniformity. What identifies a tiling when its vertex configuration cannot, and where the search hits its limit.