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Symmetry elements of crystals
Short answer
Symmetry elements include planes of symmetry (mirror planes), axes of symmetry (rotation: diad, triad, tetrad, hexad), and centre of symmetry. A cube has 9 planes, 13 axes, and 1 centre, defining its isometric crystal system.
Describe the symmetry elements of crystals.
Symmetry in a crystal is the repetition of faces, edges and angles when the crystal is rotated or reflected. The imaginary features about which this repetition occurs are the elements of symmetry.
1. Plane of symmetry
An imaginary plane that divides a crystal into two equal halves, each the mirror image of the other.
- Axial (principal) plane: passes through two crystallographic axes.
- Diagonal plane: passes through one axis and bisects the angle between two others.
- A cube has 9 planes (3 axial, 6 diagonal).
2. Axis of symmetry
An imaginary line through the centre about which the crystal, when rotated through 360°, shows the same appearance more than once.
| Axis | Repeats | Rotation angle |
|---|---|---|
| Diad (2-fold) | 2 times | 180° |
| Triad (3-fold) | 3 times | 120° |
| Tetrad (4-fold) | 4 times | 90° |
| Hexad (6-fold) | 6 times | 60° |
A cube has 3 tetrad, 4 triad and 6 diad axes, total 13 axes.
3. Centre of symmetry
A point at the centre of the crystal such that any line through it meets identical faces, edges or corners at equal distances on opposite sides. A cube has 1 centre.
Cube (isometric): 9 P + 13 A + 1 C = 23 elements
P = planes, A = axes, C = centre
The symmetry of a crystal decides which of the 7 crystal systems it belongs to.
✓ Answer checked by Claude Opus 5.5 (high effort)
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