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A004030 Number of n-dimensional Bravais lattices.
(Formerly M3847)
0
1, 1, 5, 14, 64, 189, 826 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

In 1850, Bravais demonstrated that crystals were comprised of 14 different types of unit cells: simple cubic, body-centered cubic, face-centered cubic; simple tetragonal, body-centered tetragonal; simple monoclinic, end-centered monoclinic; simple orthorhombic, body-centered orthorhombic, face-centered orthorhombic, end-centered orthorhombic; rhombohedral; hexagonal; and triclinic. [From Jonathan Vos Post, Mar 09 2010]

REFERENCES

H. Brown, R. B\"{u}low, J. Neub\"{u}ser, 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.

W. Plesken and W. Hanrath, The lattices of six-dimensional space, Math. Comp., 43 (1984), 573-587.

Lomont, J. S. "Crystallographic Point Groups." 4.4 in Applications of Finite Groups. New York: Dover, pp. 132-146, 1993. [From Jonathan Vos Post, Mar 09 2010]

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

Souvignier, B. "Enantiomorphism of Crystallographic Groups in Higher Dimensions with Results in Dimensions Up to 6." Acta Cryst. A 59, 210-220, 2003. [From Jonathan Vos Post, Mar 09 2010]

Yale, P. B. "Crystallographic Point Groups." 3.4 in Geometry and Symmetry. New York: Dover, pp. 103-108, 1988. [From Jonathan Vos Post, Mar 09 2010]

LINKS

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

Pegg, Ed Jr., Bravais Lattice. [From Jonathan Vos Post, Mar 09 2010]

Dr 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 [From Gerald McGarvey, Mar 25 2010]

CROSSREFS

Sequence in context: A165517 A197788 A197661 * A194994 A166795 A128102

Adjacent sequences:  A004027 A004028 A004029 * A004031 A004032 A004033

KEYWORD

nonn,hard,nice

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 18 11:35 EDT 2014. Contains 240707 sequences.