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A006227 Number of n-dimensional space groups (including enantiomorphs).
(Formerly M2104)
1, 2, 17, 230, 4894, 222097 (list; graph; refs; listen; history; text; internal format)



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).


Table of n, a(n) for n=0..5.

Dror Bar-Natan, Illustrations of 2-dimensional symmetry groups

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, CARAT Homepage

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.

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)

Wikipedia, Space group


Cf. A004027, A004029.

Sequence in context: A144208 A183711 A058239 * A036082 A240999 A099694

Adjacent sequences:  A006224 A006225 A006226 * A006228 A006229 A006230




N. J. A. Sloane


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



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Last modified November 26 20:03 EST 2015. Contains 264509 sequences.