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A004029 Number of n-dimensional space groups.
(Formerly M2103)
1, 2, 17, 219, 4783, 222018, 28927915 (list; graph; refs; listen; history; text; internal format)



Right border of A293060. - Andrey Zabolotskiy, Oct 07 2017


H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space. Wiley, NY, 1978, p. 52.

C. Cid, T. Schulz: Computation of Five and Six Dimensional Bieberbach Groups, Experimental Mathematics 10:1 (2001), 109-115

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 and 934.

T. Janssen, Crystallographic Groups. North-Holland, Amsterdam, 1973, p. 119.

R. L. E. Schwarzenberger, N-Dimensional Crystallography. Pitman, London, 1980, p. 34.

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..6.

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

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.

E. S. Rosenthal & N. J. A. Sloane, Correspondence, 1975

R. L. E. Schwarzenberger, Colour symmetry, Bulletin of the London Mathematical Society 16.3 (1984): 216-229.

Wikipedia, Space group

Index entries for sequences related to groups


Cf. A006227, A004027, A293060.

Sequence in context: A126752 A234461 A277768 * A114268 A144208 A183711

Adjacent sequences:  A004026 A004027 A004028 * A004030 A004031 A004032




N. J. A. Sloane


a(6) corrected by W. Plesken and T. Schulz. Thanks to Max Horn for reporting this correction, Dec 18 2009



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Last modified October 15 01:40 EDT 2019. Contains 328025 sequences. (Running on oeis4.)