A006227 Number of n-dimensional space groups (including enantiomorphs).

1, 2, 17, 230, 4894, 222097

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more
• nice

Comments

Right border of A293061. - Andrey Zabolotskiy, Oct 07 2017

References

• Colin Adams, The Tiling Book, AMS, 2022; see p. 59.
• H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space. Wiley, NY, 1978, p. 52.
• P. Engel, Geometric crystallography, in P. M. Gruber and J. M. Wills, editors, Handbook of Convex Geometry. North-Holland, Amsterdam, Vol. B, pp. 989-1041.
• J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 102.
• T. Janssen, Crystallographic Groups. North-Holland, Amsterdam, 1973, p. 119.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Dror Bar-Natan, Illustrations of 2-dimensional symmetry groups
• Manuel Caroli and Monique Teillaud. Delaunay triangulations of closed Euclidean dorbifolds. Discrete and Computational Geometry, Springer Verlag, 2016, 55 (4), pp.827-853. 10.1007/s00454-016-9782-6, hal-01294409
• J. Neubüser, B. Souvignier and H. Wondratschek, Corrections to Crystallographic Groups of Four-Dimensional Space by Brown et al. (1978) [New York: Wiley and Sons], Acta Cryst., A58 (2002), 301.
• J. Opgenorth, W. Plesken and T. Schulz, Crystallographic Algorithms and Tables, Acta Cryst., A54 (1998), 517-531.
• W. Plesken, J. Opgenorth and T. Schulz, CARAT - a package for mathematical crystallography, Journal of Applied Crystallography, 31 (1998), 827-828.
• W. Plesken and T. Schulz, Dominik Bernhardt and others, Computer package CARAT
• W. Plesken and T. Schulz, CARAT Homepage [dead link]
• W. Plesken and T. Schulz, CARAT Homepage [Cached copy in pdf format (without subsidiary pages), with permission]
• W. Plesken and T. Schulz, Introduction to CARAT [Cached copy in pdf format (without subsidiary pages), with permission]
• W. Plesken and T. Schulz, Counting crystallographic groups in low dimensions, Experimental Mathematics 9 (No. 3, 2000) 407-411.
• E. S. Rosenthal & N. J. A. Sloane, Correspondence, 1975
• B. Souvignier, Enantiomorphism of crystallographic groups in higher dimensions with results in dimensions up to 6, Acta Cryst., A59 (2003), 210-220.
• The Fascination of Crystals and Symmetry, 230 (The space group list project)
• N. A. Vavilov, Saint Petersburg School of the Theory of Linear Groups. I. Prehistory, Vestnik St. Petersburg Univ. (Russia 2023), Vol. 56, 273-288.
• Wikipedia, Space group
• Index entries for sequences related to groups

Crossrefs

Cf. A004027, A004029, A293061.

Extensions

a(4) corrected according to Neubüser, Souvignier and Wondratschek (2002) - Susanne Wienand, May 19 2014

a(5) added according to Souvignier (2003); a(6) should not be extracted from that paper because it uses the old incorrect CARAT data for d=6 - Andrey Zabolotskiy, May 19 2015