The 230 space groups, by number and symbol — SymmeTry

The 230 space groups, by number and symbolAll 230 space groups by number and Hermann-Mauguin symbol: crystal system, lattice centring, general positions, and the cell you can build in each.Molecular point groups with their operations and character tables, the 230 space groups with a cell builder, and the 17 wallpaper and 7 frieze groups drawn live. The tool needs JavaScript, and WebGL2 for the 3D views; these are the pages it offers:

Molecules — the point group of a molecule, in 3D

Crystals — build a cell in any of the 230 space groups

Plane — name the symmetry of a repeating pattern

Tutorial — from a mirror plane to a space group

Exercises — checked, with hints and an answer

Cheatsheet — printable, one page

Point groups — operations, order and character table

Space groups — all 230, by number and symbol

Wallpaper groups — the seventeen, drawn

Frieze groups — the seven, drawn

About — what it computes, and what it borrows

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