Cryst

Computing with crystallographic groups

4.1.32

18 August 2026

Bettina Eick
Email: beick@tu-bs.de
Homepage: http://www.iaa.tu-bs.de/beick
Address:
Institut Analysis und Algebra, TU Braunschweig
Universitätsplatz 2, D-38106 Braunschweig, Germany

1 Introduction

2 Affine crystallographic groups

2.1 The default action

2.1-1 SetCrystGroupDefaultAction

2.2 Construction

  2.2-1 AffineCrystGroupOnRight
  2.2-2 AsAffineCrystGroupOnRight
  2.2-3 IsAffineCrystGroupOnRight
  2.2-4 AffineCrystGroupOnLeft
  2.2-5 AsAffineCrystGroupOnLeft
  2.2-6 IsAffineCrystGroupOnLeft
  2.2-7 AffineCrystGroup
  2.2-8 AsAffineCrystGroup
  2.2-9 IsAffineCrystGroup
  2.2-10 TransposedMatrixGroup

2.3 Point group

  2.3-1 PointGroup
  2.3-2 IsPointGroup
  2.3-3 AffineCrystGroupOfPointGroup
  2.3-4 PointHomomorphism
  2.3-5 IsPointHomomorphism

2.4 Translation lattice

  2.4-1 TranslationBasis
  2.4-2 InternalBasis
  2.4-3 AddTranslationBasis
  2.4-4 CheckTranslationBasis
  2.4-5 IsSpaceGroup
  2.4-6 IsStandardAffineCrystGroup
  2.4-7 IsStandardSpaceGroup
  2.4-8 StandardAffineCrystGroup
  2.4-9 IsSymmorphicSpaceGroup

2.5 Special methods

  2.5-1 \^
  2.5-2 IsomorphismFpGroup
  2.5-3 IsomorphismFpGroup
  2.5-4 IsomorphismPcpGroup
  2.5-5 IsomorphismPcpGroup

2.6 Maximal subgroups

2.6-1 MaximalSubgroupClassReps
2.6-2 ConjugacyClassesMaximalSubgroups

2.7 Space groups with a given point group

  2.7-1 SpaceGroupsByPointGroupOnRight
  2.7-2 SpaceGroupTypesByPointGroupOnRight
  2.7-3 SpaceGroupsByPointGroupOnLeft
  2.7-4 SpaceGroupTypesByPointGroupOnLeft
  2.7-5 SpaceGroupsByPointGroup
  2.7-6 SpaceGroupTypesByPointGroup

2.8 Wyckoff positions

  2.8-1 WyckoffPositions
  2.8-2 WyckoffPositionsByStabilizer
  2.8-3 IsWyckoffPosition
  2.8-4 WyckoffBasis
  2.8-5 WyckoffTranslation
  2.8-6 WyckoffSpaceGroup
  2.8-7 WyckoffStabilizer
  2.8-8 WyckoffOrbit
  2.8-9 WyckoffGraph

2.9 Normalizers

  2.9-1 NormalizerPointGroupInGLnZ
  2.9-2 CentralizerPointGroupInGLnZ
  2.9-3 TranslationNormalizer
  2.9-4 AffineNormalizer
  2.9-5 AffineInequivalentSubgroups
  2.9-6 ConjugatorSpaceGroups

2.10 Color groups

  2.10-1 ColorGroup
  2.10-2 IsColorGroup
  2.10-3 ColorSubgroup
  2.10-4 ColorCosetList
  2.10-5 ColorOfElement
  2.10-6 ColorPermGroup
  2.10-7 ColorHomomorphism
  2.10-8 Subgroup

2.11 Colored AffineCrystGroups

2.11-1 PointGroup

2.12 International Tables

  2.12-1 SpaceGroupSettingsIT
  2.12-2 SpaceGroupOnRightIT
  2.12-3 SpaceGroupOnLeftIT
  2.12-4 SpaceGroupIT

References

Index

Cryst

Computing with crystallographic groups

Contents