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AClib

Almost Crystallographic Groups - A Library and Algorithms

1.4

12 August 2026

Karel Dekimpe
Email: Karel.Dekimpe@kuleuven.be
Homepage: https://kulak.kuleuven.be/~dekimpe/
Address:
Katholieke Universiteit Leuven
Campus Kortrijk, Universitaire Campus
Kortrijk, B 8500
Belgium

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

Contents

1 The Almost Crystallographic Groups Package

1.1 More about almost crystallographic groups

2 Algorithms for almost crystallographic groups

2.1 Properties of almost crystallographic groups

2.1-1 IsAlmostCrystallographic
2.1-2 IsAlmostBieberbachGroup

2.2 Betti numbers

  2.2-1 OrientationModule
  2.2-2 BettiNumber
  2.2-3 BettiNumbers

2.3 Determination of certain extensions

2.3-1 HasExtensionOfType

3 The catalog of almost crystallographic groups

3.1 Rational matrix groups

3.1-1 AlmostCrystallographicGroup

3.2 Polycyclically presented groups

  3.2-1 AlmostCrystallographicPcpGroup
  3.2-2 IsomorphismPcpGroup
  3.2-3 HolonomyGroup

3.3 More about the type and the defining parameters

3.3-1 AlmostCrystallographicInfo

3.4 The electronic versus the printed library

4 Example computations with almost crystallographic groups

4.1 Example computations I

4.2 Example computations II

4.3 Example computations III

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