This site is supported by donations to The OEIS Foundation.



Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A004030 Number of n-dimensional Bravais lattices.
(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) is a(6) = 841 (not 826). - Vaclav Kotesovec, Sep 29 2014


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.

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]

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


Sequence in context: A165517 A197788 A197661 * A194994 A166795 A128102

Adjacent sequences:  A004027 A004028 A004029 * A004031 A004032 A004033




N. J. A. Sloane



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 21 09:07 EST 2014. Contains 252300 sequences.