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A004029 Number of n-dimensional space groups.
(Formerly M2103)
9
1, 2, 17, 219, 4783, 222018, 28927915 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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).

LINKS

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.

Wikipedia, Space group

Index entries for sequences related to groups

CROSSREFS

Cf. A006227, A004027, A092240.

Sequence in context: A126752 A234461 A277768 * A114268 A144208 A183711

Adjacent sequences:  A004026 A004027 A004028 * A004030 A004031 A004032

KEYWORD

nonn,hard,more,nice

AUTHOR

N. J. A. Sloane, Apr 30 1991

EXTENSIONS

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

STATUS

approved

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Last modified December 9 14:26 EST 2016. Contains 278971 sequences.