Alicatado is the technique of cutting individual pieces of glazed tile to shape and setting them into geometric mosaic, the method behind Moroccan zellige and the Alhambra dados. It differs from painted tile in that each shape is a separately cut piece of fired ceramic. The bone tiling is an alicatado pattern: its curved tiles are cut pieces, not lines painted on a square tile.

The mathematics · 30 August 2026

The bones of the Alhambra.

Q: Is curved Islamic geometry still compass-and-straightedge?

Yes, and the bone tiling is the clearest proof. Every curved edge is a circular arc, and for the canonical Alhambra bone every arc's centre lands on a point of the tile grid while its radius equals the tile's half-diagonal. That means a craftsman can scribe the entire wall with one compass opening, striking each curve from a lattice point. The pattern has no straight edges yet is genuinely compass work, so the phrase derived, not generated holds with no asterisk.

Almost everything in Islamic geometry is built from straight lines. The hueso - Spanish for bone - is the great exception: a Nasrid cut-tile pattern from the dados of the Alhambra made entirely of curves, a checkerboard of interlocking bone-shaped tiles. And here is the good part. It has not one straight edge, and it is still, provably, compass work.

FIG. 1 - The hueso tiling, drawn live. Each tile is bitten concave on two sides by its neighbours and bulges convex on the other two, so they lock together with no gaps.

The tiles are the pattern

Most of what this studio makes is strapwork: a network of lines laid over an underlying grid, the grid then rubbed out. The hueso is a different kind of object. It is alicatado - cut-tile mosaic, the same craft as Moroccan zellige - and there is no line network at all. The deliverable is the tiles themselves, each a curved piece of glazed ceramic cut to shape and set against its neighbours. What makes it a bone is that every edge is a circular arc: two of them curve inward, as if a neighbour has taken a bite, and two bulge outward to fill the bites of the tiles on the other two sides. Bites and bulges pair off exactly, so the wall closes with no gaps and no leftover ground.

One compass, one setting

Now the fact that makes this pattern belong on a page about mathematics. Every one of those arcs is part of a circle, and you might expect each to need its own centre and its own radius, carefully placed. They do not. For the canonical Alhambra bone, every arc is struck with a single compass opening: its radius is exactly the tile's half-diagonal, and its centre lands precisely on a point of the square grid the tiles sit on. A craftsman sets the compass once, to the half-diagonal, and scribes the entire wall - each bite from the neighbouring tile's centre, each bulge from the tile's own.

That is why the hueso is the cleanest possible answer to anyone who hears "derived, not generated" and reaches for the obvious objection - surely the curves, at least, are drawn by feel? No. The curves are the most rigorously constructed thing in the whole studio: a lattice point and a fixed radius, nothing placed by eye. The brand line holds here with no asterisk, on a pattern that is nothing but curves.

THE BONE TILING, IN ONE SENTENCE - a curved cut-tile mosaic whose every arc is scribed from a single compass setting, so a pattern with no straight edges is still pure compass-and-straightedge.

FIG. 2 - The same tiling in an Alhambra glaze register. The geometry is identical; only the colour assignment by class changes.

Curves that a machine can cut

Because the arcs are exact, they stay exact all the way to the workshop. When the studio writes a fabrication file for a bone tiling, the curved edges go out as true arcs, not as many little straight segments pretending to be a curve. A waterjet or CNC router reads the real circle and cuts a clean edge, and the smallest waist of each bone - the pinch where the two bites come closest - is reported in millimetres so a maker knows the tile will survive being cut. The pattern that was scribed with one compass opening seven centuries ago exports as one radius today. That is the whole idea of this studio, on its most beautiful exception.

The series

Back to the beginning: the number that keeps appearing The trisection that arrives, uninvited, across four separate constructions - and what it tells us about the tradition.

Cut a bone tiling yourself.

Build the Alhambra hueso, recolour it by class, and export true-arc fabrication files - free to explore in the browser.

Open the studio

Common questions

What is the Alhambra bone tiling (hueso)?

The hueso, Spanish for bone, is a Nasrid cut-tile pattern from the dado tilework of the Alhambra in Granada: a checkerboard of interlocking bone-shaped tiles, each bitten concave on two sides and bulging convex on the other two, locking together with no gaps. The curved tiles themselves are the pattern; there is no overlaid line network.

Is curved Islamic geometry still compass-and-straightedge?

Yes, and the bone tiling proves it. Every curved edge is a circular arc whose centre lands on a point of the tile grid and whose radius equals the tile's half-diagonal, so a craftsman scribes the whole wall with one compass opening. The pattern has no straight edges yet is genuinely compass work.

What is alicatado?

Alicatado is the technique of cutting individual pieces of glazed tile to shape and setting them into geometric mosaic, the method behind Moroccan zellige and the Alhambra dados. Each shape is a separately cut piece of fired ceramic. The bone tiling is alicatado: its curved tiles are cut pieces, not lines painted on a square tile.