login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A004030 Number of n-dimensional Bravais lattices (version 1).
(Formerly M3847)
1
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 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

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. [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]

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, 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

CROSSREFS

Cf. A256413.

Sequence in context: A165517 A197788 A197661 * A256413 A194994 A166795

Adjacent sequences:  A004027 A004028 A004029 * A004031 A004032 A004033

KEYWORD

nonn,hard,nice,more

AUTHOR

N. J. A. Sloane

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified December 8 01:14 EST 2016. Contains 278902 sequences.