A256413 - OEIS

%I #27 May 30 2026 16:40:43

%S 1,1,5,14,64,189,841

%N Number of n-dimensional Bravais lattices.

%D H. Brown, R. Bülow, J. Neubüser, H. Wondratschek and H. Zassenhaus, Crystallographic Groups of Four-Dimensional Space. Wiley, NY, 1978, p. 52.

%D 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.

%D Lomont, J. S. "Crystallographic Point Groups." 4.4 in Applications of Finite Groups. New York: Dover, pp. 132-146, 1993.

%D Yale, P. B. "Crystallographic Point Groups." 3.4 in Geometry and Symmetry. New York: Dover, pp. 103-108, 1988.

%H D. Freittloh, <a href="https://arxiv.org/abs/1305.1798">Highly symmetric fundamental cells for lattices in R^2 and R^3</a>, arXiv.1305.1798 [math.CO], 2013.

%H S. J. Heyes, <a href="http://web.archive.org/web/20120609152332im_/http://www.chem.ox.ac.uk/icl/heyes/structure_of_solids/Lecture1/Bravais.gif">Illustration of the 14 possible 3-D Bravais lattices</a> from <a href="http://web.archive.org/web/20131007080827/http://www.chem.ox.ac.uk/icl/heyes/structure_of_solids/Lecture1/Lec1.html">Lecture 1. Fundamental Aspects of Solids & Sphere Packing. - Analysing a 3D solid</a>

%H Opgenorth, J; Plesken, W; Schulz, T, <a href="https://doi.org/10.1107/S010876739701547X">Crystallographic Algorithms and Tables</a>, Acta Crystallogr. A, 54 (1998), 517-531.

%H Pegg, Ed Jr., <a href="https://mathworld.wolfram.com/BravaisLattice.html">Bravais Lattice.</a>

%H W. Plesken and W. Hanrath, <a href="https://doi.org/10.1090/S0025-5718-1984-0758205-5">The lattices of six-dimensional Euclidean space</a>, Math. Comp., 43 (1984), 573-587. [Warning: gives wrong value for a(6).]

%H B. Souvignier, <a href="https://doi.org/10.1107/S0108767303004161">Enantiomorphism of Crystallographic Groups in Higher Dimensions with Results in Dimensions Up to 6</a>, Acta Cryst. A 59, 210-220, 2003.

%H Bernd Souvignier, <a href="http://www.crystallography.fr/mathcryst/pdf/havana/Souvignier_syllabus.pdf">Space groups</a>, 2007, p. 30

%Y Cf. A004029.

%Y A004030 is an incorrect version found in the literature.

%K nonn,hard,more

%O 0,3

%A _N. J. A. Sloane_, Apr 04 2015