A004031 Number of n-dimensional crystal systems.

1, 1, 4, 7, 33, 59, 251

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• more
• nice

Comments

From Andrey Zabolotskiy, Jul 12 2017: (Start)

From Souvignier (2003): "the unions of all geometric classes intersecting the same set of Bravais flocks is defined to be a crystal system or point-group system. <...> This means that two geometric classes belong to the same crystal system if for any representative of the first class there is a representative of the other class such that the representatives have GL(n,Q)-conjugate Bravais groups. <...> The definition for crystal systems as given by Brown et al. (1978) therefore is only valid in dimensions up to 4, where it coincides with the more general definition adopted here."

For dimension 6, Souvignier (2003) uses old incorrect CARAT data, but the error affected only geometric classes and finer classification, so the data for crystal systems must be correct.

Among 33 4-dimensional crystal systems, 7 are enantiomorphic.

Coincides with the number of n-dimensional Bravais systems for n<5 (only).

(End)

References

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

Links

• H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space. Wiley, NY, 1978, p. 52. Corrections.
• J. Neubüser, W. Plesken, and H. Wondratschek, An emendatory discussion on defining crystal systems, Commun. Math. Chem., 10 (1981), 77-96.
• W. Plesken and T. Schulz, CARAT Homepage
• W. Plesken and T. Schulz, CARAT Homepage [Cached copy in pdf format (without subsidiary pages), with permission]
• B. Souvignier, Enantiomorphism of crystallographic groups in higher dimensions with results in dimensions up to 6, Acta Cryst., A59 (2003), 210-220.

Crossrefs

Cf. A004026-A004029, A004032, A006226, A006227, A080738.

Extensions

a(5)-a(6) from Souvignier (2003) by Andrey Zabolotskiy, Jul 12 2017