Related Experiment Video
Updated: Jun 2, 2026

Sample Preparation and Transfer Protocol for In-Vacuum Long-Wavelength Crystallography on Beamline I23 at Diamond Light Source
Published on: April 23, 2021
Exact direct-space asymmetric units for the 230 crystallographic space groups
Ralf W Grosse-Kunstleve1, Buddy Wong, Marat Mustyakimov
1Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720-8118, USA. rwgrosse-kunstleve@lbl.gov
Abstract:
It is well known that the direct-space asymmetric unit definitions found in the International Tables for Crystallography, Volume A, are inexact at the borders. Face- and edge-specific sub-conditions have to be added to remove parts redundant under symmetry. This paper introduces a concise geometric notation for asymmetric unit conditions. The notation is the foundation for a reference table of exact direct-space asymmetric unit definitions for the 230 crystallographic space-group types. The change-of-basis transformation law for the conditions is derived, which allows the information from the reference table to be used for any space-group setting. We also show how the vertices of an asymmetric unit can easily be computed from the information in the reference table.
Related Concept Videos
Unit Cells
The Seven Crystal Systems: Overview
Crystallographic Point Groups
Structures of Solids
Symmetry Elements in a Crystal
Law of Rational Indices

