A256413 Number of n-dimensional Bravais lattices.

1, 1, 5, 14, 64, 189, 841

Offset

0,3

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.

Lomont, J. S. "Crystallographic Point Groups." 4.4 in Applications of Finite Groups. New York: Dover, pp. 132-146, 1993.

Yale, P. B. "Crystallographic Point Groups." 3.4 in Geometry and Symmetry. New York: Dover, pp. 103-108, 1988.

Links

Table of n, a(n) for n=0..6.

D. Freittloh, Highly symmetric fundamental cells for lattices in R^2 and R^3, arXiv.1305.1798 [math.CO], 2013.

S. J. Heyes, Illustration of the 14 possible 3-D Bravais lattices from Lecture 1. Fundamental Aspects of Solids & Sphere Packing. - Analysing a 3D solid

Opgenorth, J; Plesken, W; Schulz, T, Crystallographic Algorithms and Tables, Acta Crystallogr. A, 54 (1998), 517-531.

Pegg, Ed Jr., Bravais Lattice.

W. Plesken and W. Hanrath, The lattices of six-dimensional Euclidean space, Math. Comp., 43 (1984), 573-587. [Warning: gives wrong value for a(6).]

B. Souvignier, Enantiomorphism of Crystallographic Groups in Higher Dimensions with Results in Dimensions Up to 6, Acta Cryst. A 59, 210-220, 2003.

Bernd Souvignier, Space groups, 2007, p. 30

Crossrefs

Cf. A004029.

A004030 is an incorrect version found in the literature.

Sequence in context: A197788 A197661 A004030 * A346212 A324011 A194994

Adjacent sequences: A256410 A256411 A256412 * A256414 A256415 A256416

Keyword

nonn,hard,more

Author

N. J. A. Sloane, Apr 04 2015

Status

approved