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A006227 Number of n-dimensional space groups (including enantiomorphs).
(Formerly M2104)

%I M2104

%S 1,2,17,230,4894,222097

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

%C Right border of A293061. - _Andrey Zabolotskiy_, Oct 07 2017

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

%D 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.

%D J. E. Goodman and J. O'Rourke, editors, Handbook of Discrete and Computational Geometry, CRC Press, 1997, p. 102.

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

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Dror Bar-Natan, <a href="http://www.math.toronto.edu/~drorbn/Gallery/Symmetry/Tilings/index.html">Illustrations of 2-dimensional symmetry groups</a>

%H Manuel Caroli, Monique Teillaud. <a href="https://hal.inria.fr/hal-01294409/document">Delaunay triangulations of closed Euclidean dorbifolds</a>. Discrete and Computational Geometry, Springer Verlag, 2016, 55 (4), pp.827-853. 10.1007/s00454-016-9782-6, hal-01294409

%H J. Neubüser, B. Souvignier and H. Wondratschek, <a href="http://dx.doi.org/10.1107/S0108767302001368">Corrections to Crystallographic Groups of Four-Dimensional Space by Brown et al. (1978) [New York: Wiley and Sons]</a>, Acta Cryst., A58 (2002), 301.

%H J. Opgenorth, W. Plesken and T. Schulz, <a href="http://dx.doi.org/10.1107/S010876739701547X">Crystallographic Algorithms and Tables</a>, Acta Cryst., A54 (1998), 517-531.

%H W. Plesken, J. Opgenorth and T. Schulz, <a href="http://dx.doi.org/10.1107/S0021889897019468">CARAT - a package for mathematical crystallography</a>, Journal of Applied Crystallography, 31 (1998), 827-828.

%H W. Plesken and T. Schulz, <a href="http://wwwb.math.rwth-aachen.de/carat/">CARAT Homepage</a>

%H W. Plesken and T. Schulz, <a href="/A006226/a006226.pdf">CARAT Homepage</a> [Cached copy in pdf format (without subsidiary pages), with permission]

%H W. Plesken and T. Schulz, <a href="/A006226/a006226_1.pdf">Introduction to CARAT</a> [Cached copy in pdf format (without subsidiary pages), with permission]

%H W. Plesken and T. Schulz, <a href="http://projecteuclid.org/euclid.em/1045604675">Counting crystallographic groups in low dimensions</a>, Experimental Mathematics 9 (No. 3, 2000) 407-411.

%H E. S. Rosenthal & N. J. A. Sloane, <a href="/A004028/a004028.pdf">Correspondence, 1975</a>

%H B. Souvignier, <a href="http://dx.doi.org/10.1107/S0108767303004161">Enantiomorphism of crystallographic groups in higher dimensions with results in dimensions up to 6</a>, Acta Cryst., A59 (2003), 210-220.

%H The Fascination of Crystals and Symmetry, <a href="http://crystalsymmetry.wordpress.com/230-2/">230 (The space group list project)</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Space_group#Classification_in_small_dimensions">Space group</a>

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

%Y Cf. A004027, A004029, A293061.

%K nonn,hard,more,nice

%O 0,2

%A _N. J. A. Sloane_

%E a(4) corrected according to Neubüser, Souvignier and Wondratschek (2002) - _Susanne Wienand_, May 19 2014

%E 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 December 17 21:59 EST 2017. Contains 296120 sequences.