Operations fall into classes — SymmeTry

Operations fall into classesSix operations, three columns: E, 2C3, 3σv. Step 9 of 18 of the symmetry tutorial, worked in a live 3D view. Change any of it and the view follows.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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