Stamping one glyph through all seventeen plane groups

Palette — plate, ink, and two kinds of mark

The scheme is argued from letterpress furniture: a dark steel plate, one pale ink, and the two colours a plate-maker would scribe in. Teal is reserved for lines — mirrors solid, glides dashed — and brass for point marks, the rotation centres. Body text never borrows the accent colours; it has its own ink so small labels stay above 4.5:1 on the plate.

Type — the specimen is the subject

Technique — symmetry as arithmetic, marks as theorems

mirror glide 2-fold 3-fold 4-fold 6-fold

Everything is canvas 2D — no libraries. Each of the seventeen groups is stored as its textbook operation set: integer 2×3 matrices in lattice coordinates, exactly as the International Tables list them (p4g, for instance, is the four rotations of p4 plus the same four reflections shifted by ½,½). A basis matrix B per lattice class — oblique, rectangular, rhombic, square, hexagonal — maps cell coordinates to pixels, and each operation's screen transform is the conjugation L = B·M·B⁻¹, handed straight to ctx.setTransform. The ampersand lives on one offscreen 320px canvas, re-rasterised every frame at the breathing weight, then stamped hundreds of times per group; where an operation's determinant is negative the stamp prints left-handed — a chiral ampersand no font menu contains, and the site's second read.

The construction marks are the part I refused to hand-draw. For every operation the code solves for its fixed locus: rotations solve (I−L)c = τ for the centre point and take the trace for its order; reflections split their translation into components along and normal to the axis direction φ = ½·atan2 of the linear part, and the smallest parallel component over all lattice copies decides solid mirror or dashed glide. So the marks are not an illustration of the group — they are computed from it, and a wrong matrix would draw its own accusation. A test hook asserts the derived mirror/glide/rotation census for all seventeen groups against the crystallographic table on every build.

Choreography: each group floods outward from the centre — stamps pop in distance-ordered with a cubic ease — then cell outline, axes and centres fade up over the ink. The cycle rests 5.4 seconds per group (9.5 on the opening p6m, so the first frame a visitor or a thumbnail sees is the full kaleidoscope, flooded, marks up). Labels swap through a 180ms opacity dip; the census cards and the 17-stop rail jump the plate to any group directly.

Iteration log