Laves tiling generator

Tilings of pentagons, kites and rhombi, built as the mirror image of the Archimedean tilings. Choose the Cairo pentagonal tiling, the rhombille or another of the eight Laves tilings, set the joints and colors, and export a seamless pattern as SVG, PNG or CSS.

Open in the generator How it works

Cairo pentagonal tiling in red, teal and ochre

What are Laves tilings?

Every tiling has a dual. Put a point in the middle of every tile, and join the points of tiles that share an edge: the new lines outline a new tiling. The dual of an Archimedean tiling, made of regular polygons, is called a Laves tiling, after the crystallographer Fritz Laves. They are also known as Catalan tilings, as the dual solids of the Archimedean polyhedra were studied by Eugène Catalan.

Where the Archimedean tilings have regular tiles with different corners, the Laves tilings have identical corners but different tiles. The result is some of the most recognizable patterns of tilework: the Cairo pentagonal tiling, which covers streets in Cairo, and the rhombille, three rhombi that look like a field of cubes.

How the generator builds them

Ornamatic takes an Archimedean tiling and draws one tile for every vertex of it: the tile is bounded by the centers of the polygons that meet at that vertex. Corners of the original tiling with three polygons give triangles; with four, kites or rhombi; with five, pentagons. The tiles then repeat exactly, so the tile is seamless.

Each kind of tile can be given its own color, or the tiles can be colored by the number of sides. A joint of your chosen width separates them, and the background shows through it.

What you can adjust

Tiling — rhombille, tetrakis square, triakis triangular, deltoidal trihexagonal, kisrhombille, Cairo pentagonal, prismatic pentagonal or floret pentagonal.
Draw — filled tiles with joints, or outlines only.
Joint or line thickness — the gap between tiles, or the line width.
Colors — by kind of tile, by number of sides, mixed at random, or one color; any palette.