ShaneLogic/Crystallographic Symmetry Notation
.claude/skills/crystallographic-symmetry-notation/SKILL.md
Decode and interpret Hermann-Mauguin symmetry notation for crystallographic point groups and space groups. Use this skill when encountering symmetry symbols like '4/m', '3m', or '6/mmm' and needing to identify the rotational axes, mirror planes, and inversion centers they represent.
$ install --global
skillsauthnpx skillsauth add ShaneLogic/SolarLab Crystallographic Symmetry NotationInstall this skill globally with one command. Works with Claude Code, Cursor, and Windsurf.
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SKILL.md
- name:
- Crystallographic Symmetry Notation
- description:
- Decode and interpret Hermann-Mauguin symmetry notation for crystallographic point groups and space groups. Use this skill when encountering symmetry symbols like '4/m', '3m', or '6/mmm' and needing to identify the rotational axes, mirror planes, and inversion centers they represent.
Crystallographic Symmetry Notation
Decode Hermann-Mauguin symmetry symbols to identify crystallographic symmetry elements.
When to Use
- Interpreting crystallographic point group symbols
- Analyzing molecular symmetry notation
- Converting symmetry descriptions to structural features
- Identifying symmetry operations in crystal structures
Symbol Components
| Component | Meaning | |-----------|---------| | n (number) | n-fold rotational symmetry axis | | m | Mirror plane | | n̄ (overbar) | Inversion axis (roto-inversion) | | I | Inversion center |
Decoding Procedure
Step 1: Identify Components
Parse the symbol into numbers (n) and letters (m).
Step 2: Interpret Numbers
- n indicates rotational symmetry
- n̄ (overbar) indicates roto-inversion
- The position of each number refers to a specific crystallographic direction
Step 3: Interpret Mirror Planes
Determine mirror plane orientation based on position relative to rotational axis:
| Notation | Meaning | |----------|---------| | m (without subscript) | Mirror plane parallel to rotational axis | | mₙ | Mirror plane perpendicular to n-fold axis | | Repeated m | Symmetry about other orthogonal planes |
Step 4: Analyze Symbol Structure
For multi-position symbols:
- First position: Primary axis symmetry
- Second position: Secondary axes or planes
- Third position: Tertiary symmetry elements
Common Examples
| Symbol | Interpretation | |--------|---------------| | 1 | No symmetry (triclinic) | | 1̄ | Inversion center only | | m | Single mirror plane | | 2 | Twofold rotation axis | | 2/m | Twofold axis with perpendicular mirror | | 3m | Threefold axis with parallel mirrors | | 4/mmm | Fourfold axis, perpendicular mirror, two sets of parallel mirrors | | 6/mmm | Sixfold axis with full hexagonal symmetry |
Output
Provide:
- List of symmetry elements present
- Orientation of each mirror plane (parallel/perpendicular to axis)
- Order of rotational axes
- Presence or absence of inversion center
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