Counting Crystallographic Groups in Low Dimensions

DOI10.1080/10586458.2000.10504417zbMath0965.20031OpenAlexW2043622719WikidataQ56286400 ScholiaQ56286400MaRDI QIDQ4526083

Tilman Schulz, Wilhelm Plesken

Publication date: 9 May 2001

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1045604675

zbMATH Keywords

crystallographic groupsBieberbach groupscomputational group theoryCARAT

Mathematics Subject Classification ID

Other geometric groups, including crystallographic groups (20H15) Software, source code, etc. for problems pertaining to group theory (20-04)

Related Items (15)

Rationality Problem for Algebraic Tori ⋮ Burckhardtian determination of the space groups. I. ⋮ Burckhardtian determination of the space groups. II. ⋮ Teichmüller theory and collapse of flat manifolds ⋮ D-V cells and fundamental domains for crystallographic groups, algorithms, and graphic real\-i\-za\-tions. ⋮ On cohomology of crystallographic groups with cyclic holonomy of split type. ⋮ Distinguishing crystallographic groups by their finite quotients ⋮ Classification of 6-dimensional splittable flat solvmanifolds ⋮ Computation of Five-and Six-Dimensional Bieberbach Groups ⋮ Crystallographic actions on Lie groups and post-Lie algebra structures ⋮ Algorithms for crystallographic groups ⋮ Fibered orbifolds and crystallographic groups ⋮ \(G_2\)-structures on flat solvmanifolds ⋮ Dual Cones and the Voronoi Algorithm ⋮ Multiplicative Invariant Fields of Dimension ≤6

Uses Software

• Magma
• CARAT

Cites Work

• Unnamed Item
• Computing isometries of lattices
• Über einen Algorithmus zur Bestimmung der Raumgruppen
• Computation of Five-and Six-Dimensional Bieberbach Groups
• Crystallographic Algorithms and Tables
• The lattices of six-dimensional Euclidean space

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