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

1, 2, 17, 230, 4894, 222097

Offset

0,2

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

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

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.

Sequence in context: A144208 A183711 A058239 * A307289 A036082 A240999

Adjacent sequences: A006224 A006225 A006226 * A006228 A006229 A006230

Keyword

nonn,hard,more,nice

Author

N. J. A. Sloane

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

Status

approved