Stereotomy — the science of tile cutting

From ancient stonework to modern algorithms

What is stereotomy?

Stereotomy is the art and science of cutting solid materials — stone, tile, brick — to fit together within a structure. The word comes from the Greek stereos (solid) and tomia (cutting). For centuries, it was a core discipline for stonemasons building arches, vaults, and cathedral walls where every stone had to be precisely shaped to carry load and fit its neighbours.

In modern tiling, stereotomy refers to the planning and optimisation of tile cuts: deciding where the tile grid starts, how it aligns with room edges, and how to minimise waste while maintaining aesthetic quality. It's the bridge between raw geometry and a beautiful finished floor.

The core problem

A regular tile grid is infinite — it extends in all directions with perfect tiles at uniform spacing. A room is a finite polygon that cuts through this grid. Every place where the room boundary intersects a tile creates a cut. The stereotomy problem is: where should the grid be positioned relative to the room to produce the best cuts?

"Best" can mean different things depending on priorities — fewest cuts, widest minimum cut, most symmetry, or alignment with a specific architectural feature like a doorway or a focal wall.

Grid origin and offset

The simplest decision is where to anchor the grid. Three common approaches:

• Corner start: Full tiles begin at one corner. Fast to install, but the opposite corner gets whatever size cut remains — which may be a thin sliver.
• Centre alignment: The grid is centred on the room. Both sides get equal cuts. More symmetrical, wider minimum cuts, but slightly more total cutting.
• Feature alignment: The grid is positioned so that a specific element — a doorway, the centre of a bathtub, or a focal wall — gets a full tile or a symmetrical arrangement. This prioritises visual impact over material efficiency.

The one-third threshold

A foundational principle in tile stereotomy: no cut piece should be narrower than one-third of the full tile dimension. A 30 cm tile should never produce a cut narrower than 10 cm. Below this threshold, tiles are fragile, difficult to cut cleanly, and visually distracting.

Mathematically, this constrains the grid offset to a specific range. For a given room width and tile pitch, there are bands of "safe" offsets where the one-third rule holds on all walls, and bands of "dangerous" offsets that produce slivers. A stereotomy algorithm systematically searches for the best safe position.

Multi-wall optimisation

In a rectangular room with four walls, the grid offset in X and Y can be optimised independently — two one-dimensional searches. But in L-shaped and complex rooms, the walls at different positions along the same axis impose conflicting constraints. A grid offset that avoids slivers on one wall may create them on another.

This is where computational stereotomy surpasses manual planning. An algorithm can evaluate sixty or more candidate positions in milliseconds, scoring each by the minimum cut width it produces across all walls simultaneously. The winning position is the one with the widest minimum cut — the safest layout overall.

Cut classification

Not all cuts are equal. A stereotomy analysis classifies each cut tile by its size relative to the full tile:

• Full tile: No cut needed. The tile fits entirely within the room boundary.
• Standard cut: Cut in one dimension but wider than one-third. Easy to cut and install.
• Thin strip: Cut narrower than one-third. Fragile and should be avoided if possible.
• Corner cut: Cut in both dimensions (at concave corners in complex rooms). Small and potentially difficult to handle.

A cut map visualises these categories with colour coding — green for full tiles, amber for standard cuts, red for thin strips — giving the tiler a complete picture before installation begins.

Stereotomy in practice

Traditional tilers do stereotomy intuitively. They dry-lay a row of tiles, check the cut at the far wall, and adjust the starting position. Experienced tilers can estimate the optimal offset in their head for simple rooms. But for complex shapes, multiple rooms, or when comparing different tile sizes and patterns, computation is faster and more reliable.

A good tile planning tool applies stereotomy principles automatically: it finds the optimal grid position, classifies every cut, generates a colour-coded map, and produces a cutting list. The tiler gets a professional installation plan without the trial and error.

The best tile layout is one where you don't notice the cuts — every piece looks intentional, every edge is clean, and the grid flows as if the room was designed for that exact tile.