Reduce the O–H stretches — symmetry exercise 16 — SymmeTry

Reduce the O–H stretches — symmetry exercise 16Γ for water’s two O–H bonds is 2, 0, 0, 2: each operation scored by how many bonds it leaves in place. Exercise 16 of 29, checked as you type.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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