Wallpaper Group Pattern Maker (17 Symmetries)

What it is for

Every repeating flat pattern — tiles, fabrics, gift wrap, Escher prints — belongs to one of exactly 17 symmetry types, the wallpaper groups. They differ in which rotations, mirrors and glide reflections repeat the motif: p1 only shifts it, p4g spins it in a pinwheel, p6m reflects it into six-fold rosettes.

This tool lets you pick a group, a motif and a cell size and builds the pattern from the symmetry operations listed in the International Tables for Crystallography. You get one seamless repeat tile as SVG, a ready CSS background snippet and a larger preview. Copies that cross the tile edge are repeated from the neighbouring cells, so the tile joins without visible seams. You can use the preset motifs or paste your own SVG path drawn in a 0–100 box.

It is a pattern generator, not a drawing program: motifs are single filled paths.

Worked example

Choose p4g, the Leaf motif, cell width 120 px, motif size 30 %, position 30 % / 12 %, colors #164E63 #E0A33A, background #F5EEDD. The answer: "Created a p4g wallpaper pattern: 8 symmetry operations per cell, repeat tile 120 × 120 px." Twelve leaf copies touch the tile — eight from the cell itself plus copies from neighbours that overhang the edges. Colored by operation, the leaves alternate teal and ochre around the four-fold centres.

For a hexagonal example pick p31m, motif Scalene triangle, cell 150 px, size 35 %, position 40 % / 15 %, rotation 20° and three colors. The tool reports 6 operations per cell, 22 copies and a repeat tile of 150 × 259.8076 px, with a note: the height is 150·√3, an irrational number, so a scaled CSS background can show hairline seams in some browsers while the SVG pattern stays exact.

How to read the result

• Symmetry operations per cell is the size of the group's point part in its conventional cell: 1 for p1, 4 for p4, 12 for p6m.
• Motif copies in one tile includes overhanging copies; it is always at least the number of operations.
• Repeat tile is the rectangle that tiles the plane: the cell itself for square and rectangular groups, three cells high for the oblique p1/p2, and width × width·√3 for hexagonal groups.
• Downloads: the tile SVG for image editors, the preview SVG with an SVG <pattern>, and the CSS file.

Tips and common mistakes

• Keep the motif away from mirror lines and rotation centres for clean, non-overlapping copies; move it with the position sliders.
• An asymmetric motif shows the symmetry best. A circle in p4m looks the same as in p1.
• "One color per symmetry operation" makes a colored pattern whose color symmetry is lower than its shape symmetry. Use First color only to see the pure group.
• Cell height stretch only affects oblique, rectangular and centred groups.
• For CSS use, prefer square and rectangular groups if seams appear when zooming.

FAQ

Why exactly 17?

A repeating pattern can only have 2-, 3-, 4- or 6-fold rotations, and only a few ways to combine them with mirrors and glides fit a lattice. The International Tables list exactly 17 plane groups, numbered 1 (p1) to 17 (p6m).

Why does my hexagonal CSS background show thin lines?

The tile height is width × √3, which is not a whole number of pixels. Use the SVG pattern, or choose a square group.

Can I draw my own motif?

Yes. Choose Custom SVG path and paste a path using M, L, H, V, C, S, Q, T and Z in a 0–100 box. Arcs are not accepted.

Is this available in Lumina?

Yes. Palette Studio → Color Atlas → Wallpaper pattern tiles your palette with the same engine.