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



In 1850, Bravais demonstrated that crystals comprised 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. - Jonathan Vos Post, Mar 09 2010

In the reference by Souvignier (Space groups, 2007, p. 30) a(6) is given as 841 (not 826). See A256413. - Vaclav Kotesovec, Sep 29 2014

I don't know if 826 is simply wrong, or is using a different definition of "distinct". - N. J. A. Sloane, Apr 04 2015


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. [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).

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]


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, 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 [From Gerald McGarvey, Mar 25 2010]

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

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

B. Souvignier, 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]

Bernd Souvignier, Space groups, 2007, p. 30


Cf. A256413.

Sequence in context: A165517 A197788 A197661 * A256413 A194994 A166795

Adjacent sequences:  A004027 A004028 A004029 * A004031 A004032 A004033




N. J. A. Sloane



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Last modified January 16 06:02 EST 2017. Contains 280807 sequences.