

A004030


Number of ndimensional Bravais lattices (version 1).
(Formerly M3847)


1




OFFSET

0,3


COMMENTS

In 1850, Bravais demonstrated that crystals comprised 14 different types of unit cells: simple cubic, bodycentered cubic, facecentered cubic; simple tetragonal, bodycentered tetragonal; simple monoclinic, endcentered monoclinic; simple orthorhombic, bodycentered orthorhombic, facecentered orthorhombic, endcentered 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 FourDimensional Space. Wiley, NY, 1978, p. 52.
P. Engel, ``Geometric crystallography,'' in P. M. Gruber and J. M. Wills, editors, Handbook of Convex Geometry. NorthHolland, Amsterdam, Vol. B, pp. 9891041.
Lomont, J. S. "Crystallographic Point Groups." 4.4 in Applications of Finite Groups. New York: Dover, pp. 132146, 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. 103108, 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 3D 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 sixdimensional Euclidean space, Math. Comp., 43 (1984), 573587.
B. Souvignier, Enantiomorphism of Crystallographic Groups in Higher Dimensions with Results in Dimensions Up to 6, Acta Cryst. A 59, 210220, 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



