A004029 Number of n-dimensional space groups.
1, 2, 17, 219, 4783, 222018, 28927915
Offset: 0
References
- 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 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
- Dror Bar-Natan, Illustrations of 2-dimensional symmetry groups
- Carlos Cid and Tilman Schulz, Computation of Five and Six Dimensional Bieberbach Groups, Experimental Mathematics 10:1 (2001), 109-115.
- 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.
- 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
Extensions
a(6) corrected by W. Plesken and T. Schulz. Thanks to Max Horn for reporting this correction, Dec 18 2009
Comments