A256413 Number of n-dimensional Bravais lattices.
1, 1, 5, 14, 64, 189, 841
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.
- 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
- 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
