Symmetry

Space group detection, Wyckoff position identification, and symmetry analysis using WASM-accelerated algorithms.

Source: src/lib/symmetry/

Algorithms

Two symmetry backends are available, both compiled to WASM:

Algorithm	Package	Description
Moyo	@spglib/moyo-wasm	Modern Rust reimplementation, recommended
Spglib	spglib (via WASM)	Classic C library, widely used reference

Key Functions

Space Group Detection

// Analyze structure symmetry (space group, point group, crystal system)
analyze_structure_symmetry(structure, algorithm?, tolerance?): SymmetryResult

// Get space group from structure
wasm_get_spacegroup(structure): SpaceGroupInfo

Wyckoff Positions

// Identify Wyckoff positions for all atoms
wyckoff_positions_from_moyo(structure): WyckoffResult[]

// Map Wyckoff positions to display atoms (including image atoms)
map_wyckoff_to_all_atoms(wyckoff_result, num_display_atoms): WyckoffMap

Symmetry Operations

// Apply symmetry operations to generate equivalent positions
apply_symmetry_operations(structure, operations): Site[]

// Initialize WASM module (called once)
ensure_moyo_wasm_ready(): Promise<void>

// Serialize structure for symmetry analysis
to_cell_json(structure): CellJSON

Symmetry Result

interface SymmetryResult {
  spacegroup_number: number      // International Tables number (1-230)
  spacegroup_symbol: string      // Hermann-Mauguin symbol (e.g., "Fm-3m")
  point_group: string            // Point group symbol
  crystal_system: string         // cubic, hexagonal, tetragonal, etc.
  bravais_lattice: string        // P, I, F, A, B, C, R
  wyckoff_positions: WyckoffSite[]
}

Wyckoff Display

Wyckoff positions can be used for atom coloring in the structure viewer:

• Each unique Wyckoff site gets a distinct color
• The color_mode: "wyckoff" setting activates this mode
• Helps identify symmetry-equivalent atoms visually

Bravais Lattices

The module identifies all 14 Bravais lattice types:

Symbol	Type
P	Primitive
I	Body-centered
F	Face-centered
A, B, C	Base-centered
R	Rhombohedral

Settings

Setting	Type	Default	Description
symprec	number	0.01	Symmetry precision tolerance (Angstroms)
symmetry_algorithm	string	"moyo"	Backend: "moyo" or "spglib"

Components

• SymmetryStats.svelte — Displays space group, point group, crystal system
• WyckoffTable.svelte — Table of Wyckoff positions with multiplicity, letter, and site symmetry