Intarsia knowledge

Symmetry and mirroring

Symmetry is one of the oldest ordering principles of intarsia, and wood is a material that never quite submits to it. This page shows the four kinds of symmetry, how veneer is mirrored and matched, why the grain breaks every symmetry, and when a pattern is stronger without it.

Diagram with four panels: an L-shaped piece of walnut on ash, once mirrored, once rotated four times, once translated and once glide-reflected; the grain turns with the shape — The four basic kinds of symmetry, shown on a shape that has no symmetry of its own. Watch the grain: it mirrors and turns along, and that is exactly what you will later see in the light.

The four kinds of symmetry

A pattern is symmetrical when, after a movement, it matches itself again. In the plane there are four such movements, and almost every geometric pattern, from a star to a running border, is built from them:

Reflection: the shape is mirrored across an axis, left becomes right. It is the symmetry the eye recognises fastest, and so the one where mistakes stand out most.
Rotation: the shape is turned about a point, four times by 90 degrees, say, or six times by 60. Stars, rosettes and pinwheels come about this way.
Translation: the shape is moved without turning and repeats as a unit. Bands, grids and honeycombs live on it.
Glide reflection: the shape is moved and at the same time mirrored across the direction of movement, alternately above and below. The result looks like a trail of footsteps.

Patterns combine these movements. A honeycomb translates a hexagon in two directions; an eight-pointed star joins rotation and reflection. If you know which movement carries a pattern when you design it, you also know which pieces are the same and how many different templates or files you need (working with templates).

Why the grain breaks every symmetry

On paper, a mirrored piece is identical to its partner. In wood it never is. Two pieces of the same shape have different figure, and when they are set in mirrored or rotated, their fibres run differently too. Because wood fibres throw back light differently depending on their direction, the same wood looks lighter or darker in a rotated piece (grain direction).

That means a decision before cutting. Either the grain follows the symmetry: every mirrored piece is cut with mirrored grain, and the pattern stays symmetrical in the light. Or the grain runs the same way in every piece: then the shape is symmetrical, the light is not. Both can look good. What looks bad is when the decision was never made and the grain changes at random.

A rotational symmetry with grain that turns along creates a well-known play: a pinwheel of four identical triangles of the same wood shows four different lightnesses, which change as you walk around the piece. Many historical star patterns use exactly this effect.

Book-matched, slip-matched, four-way matched

Mirroring also happens within the veneer itself, not only in the pattern. Leaves of veneer from one bundle lie in the order they were cut from the log and show almost the same figure. How two or more such leaves are laid side by side is called the match.

Diagram with three matches of walnut veneer: book-matched with mirrored figure and one lighter leaf, slip-matched with repeated figure, and four-way matched with a centre — Three matches: book-matched like an open book, slip-matched the same way round, four-way matched across two axes. In book-matched veneer every second leaf looks lighter in the light.

Book-matched: two consecutive leaves are opened out like a book. The figure mirrors at the joint and creates a clear central axis.
Slip-matched: the leaves are laid side by side the same way round. The figure repeats, and the surface looks calmer and more even in the light.
Four-way matched: four leaves are mirrored across two axes. The result is a symmetrical picture with a centre, familiar from table tops and panels. It needs four consecutive leaves.

Book-matched veneer has a quirk worth knowing. Slicing gives every leaf an open and a closed face. When every second leaf is flipped, its other face is on top, so the leaves take light and finish slightly differently and look alternately lighter and darker depending on the angle (judging veneer quality). With a single pair that is a lively effect; with many small pieces it can look restless.

Symmetry demands accuracy

The eye is very sensitive to axes of reflection. A pattern that is almost symmetrical does not look almost right; it looks wrong. So it pays to build symmetrical patterns from the axis or the centre outwards rather than from one edge: small deviations then spread to both sides instead of adding up to the far end (assembling an intarsia).

Axis first: fix and mark the axis of reflection or the point of rotation first; every measurement refers to it.
Make mirrored templates digitally: a mirrored file or printout is made on the computer, not by turning a paper template over (designing and transferring).
Mark the faces: on asymmetric pieces, mark the show face and the grain direction on every piece. Otherwise a piece turned over becomes a mirrored one.
Cut pairs together: cutting mirror-image pieces from consecutive leaves keeps their figure similar.

Colour reversal: symmetry between light and dark

Besides symmetry in space, there is one that only exists in work with several colours: the reversal of light and dark. A pattern is laid once light on a dark ground and once dark on a light ground. André-Charles Boulle already used it, cutting brass and tortoiseshell together to get two versions of the same pattern (history of intarsia).

Two FOCUS pen holders: on the left ash with a cell pattern in mahogany, on the right mahogany with a cell pattern in ash — The same cell pattern reversed: left, mahogany as the drawing on ash; right, ash as the drawing on mahogany. The cells themselves are an example of translation in two directions.

With colour reversal more than the colour changes. Dark areas look heavier and smaller, light ones lighter and larger, so the same pattern reversed looks not only different but differently weighted (contrast and colour temperature).

When asymmetry is stronger

Symmetry gives calm and dignity, but it can also look rigid. Asymmetry creates tension and movement, but it needs something else to hold it, or it looks like a mistake. That hold can be a centre, a clear balance of light and dark, or a direction the eye follows.

The wall piece Fracture from the front: shards of light, red-brown and dark woods radiate from a light centre, separated by black lines — Fracture: no axis of reflection, no repetition, no grid. The order comes from the light centre from which the shards radiate.

The Reihax wall piece Fracture shows what that can look like: it has no grid, no repetition and no symmetry, and still looks ordered, because every shard starts from one centre. Many pieces sit between the two poles. The pen holder Ich ♥ Bayern combines a translated diamond pattern with free motifs such as mountains and lettering.

Four sides of the Ich ♥ Bayern pen holder: lettering with the diamond pattern, a mountain panorama, a lion on diamonds and the saying Dahoam is Dahoam — Ich ♥ Bayern: diamonds as strict translation, mountains and lettering as free shapes on the same four sides.

Checklist for symmetrical patterns

Kind of symmetry decided: reflection, rotation, translation or glide reflection
Decided whether the grain follows the symmetry or runs the same way everywhere
Axis or centre fixed first, built outwards from there
Mirrored templates made digitally, show face and grain marked on every piece
Mirror-image pieces cut from consecutive leaves
With book-matched veneer, the alternation of light and dark leaves planned for
With asymmetry, a clear hold set: a centre, a balance or a direction

Frequently asked questions

What kinds of symmetry are there in intarsia?

Four basic kinds: reflection across an axis, rotation about a point, translation, meaning the repetition of a unit, and glide reflection, a translation combined with a reflection. Almost every geometric pattern, from stars to running borders, is built from these four movements.

What does book-matched veneer mean?

Book-matched means that two consecutive leaves of veneer from one bundle are opened out side by side like the pages of a book. The figure is mirrored at the joint. Because every second leaf has its other face on top, the leaves reflect light differently and look alternately lighter and darker depending on the angle.

What is the difference between book-matched and slip-matched?

Book-matched leaves are flipped over, so the figure mirrors at the joint. Slip-matched leaves are laid side by side the same way round, so the figure repeats. Slip-matched veneer looks calmer and more even in the light; book-matched veneer creates a clear central axis.

Does an intarsia have to be symmetrical?

No. Symmetry gives calm and order, asymmetry tension and movement. An asymmetric pattern needs something else to hold it, though: a centre, a clear balance of light and dark, or a direction. The Reihax wall piece Fracture, for example, has no grid, no repetition and no symmetry and still looks ordered.