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Symmetry Information

Symmetry Information displays the space-group symmetry of the selected crystal and renders International Tables for Crystallography Vol. A-style schematic diagrams of the symmetry elements and general positions.

Symmetry Information

The window is divided into a space-group identity area (top left), a calculation/table area with tabs (top right), and two schematic diagrams (bottom).

Space-group identity

The top-left panel lists, for the current space group:

  • Number (1–230) and the setting index
  • Crystal System
  • Point Group — Hermann–Mauguin (HM) and Schoenflies (SF) symbols
  • Space Group — HM short symbol, HM full symbol, SF symbol, and Hall symbol

Geometrics Calculation

Geometrics Calculation

Enter two planes (h₁k₁l₁, h₂k₂l₂) or two axes (u₁v₁w₁, u₂v₂w₂) to obtain:

  • the d-spacing of each plane / the length of each axis,
  • the angle between the two planes (or two axes),
  • the axis normal to both planes and the plane normal to both axes.

These calculations respect the metric of the current unit cell.

Wyckoff Positions

Wyckoff Positions

Lists every Wyckoff position with its multiplicity, Wyckoff letter, site symmetry, and representative coordinates (coset representatives for centred lattices are shown in the header row).

Conditions

Conditions

Reflection (extinction) conditions arising from the lattice centring and from the glide/screw symmetry operators.

Symmetry-element & general-position diagrams

The two panels at the bottom reproduce the schematic diagrams used in International Tables for Crystallography Vol. A.

  • Left — symmetry elements: rotation/screw axes, mirror/glide planes, inversion centres and rotoinversion points are drawn with the conventional graphical symbols.
  • Right — general positions: the general equivalent positions are plotted as +/− circles (filled comma marks denote opposite handedness), with their fractional coordinates.

Controls below the diagrams:

  • Direction (a / b / c) — choose the projection axis.
  • The displayed range can be limited (e.g. Upper left quadrant only), and the a, b, c scale factors of the general-position plot can be adjusted.
  • Copy each diagram to the clipboard as a vector image (EMF) or raster image (BMP); EMF can be ungrouped and edited in PowerPoint.

The same symmetry elements can also be drawn directly onto the 3D model in the 5. Structure viewer.