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Number of equivalence classes of reflexive polytopes in dimension n.
2

%I #49 Jan 08 2019 19:10:19

%S 1,16,4319,473800776

%N Number of equivalence classes of reflexive polytopes in dimension n.

%C Two polytopes in dimension n are called "equivalent" if there is a matrix in GL(n,Z) that carries one polytope onto the other. The 16 equivalence classes of reflexive polygons in dimension 2 are illustrated in Doran and Whitcher 2012. - _Jonathan Sondow_, Dec 08 2012

%H Ross Altman, James Gray, Yang-Hui He, Vishnu Jejjala, Brent D. Nelson. <a href="http://dx.doi.org/10.1007/JHEP02(2015)158">A Calabi-Yau database: threefolds constructed from the Kreuzer-Skarke list</a>, Journal of High Energy Physics, 2015, doi://10.1007/JHEP02(2015)158 .

%H C. F. Doran and U. A. Whitcher, <a href="http://www.jstor.org/stable/10.4169/math.mag.85.5.343">From polygons to string theory</a>, Math. Mag., 85 (2012), 343-359.

%H Amihay Hanany and Rak-Kyeong Seong, <a href="http://arxiv.org/abs/1201.2614">Brane Tilings and Reflexive Polygons</a>, arXiv:1201.2614 [hep-th], 2012.

%H YH He, V Jejjala, L Pontiggia, <a href="http://arxiv.org/abs/1512.01579">Patterns in Calabi--Yau Distributions</a>, arXiv preprint arXiv:1512.01579 [hep-th], 2015.

%H Yang-Hui He, Rak-Kyeong Seong, Shing-Tung Yau, <a href="https://arxiv.org/abs/1704.03462">Calabi-Yau Volumes and Reflexive Polytopes</a>, arXiv:1704.03462 [hep-th], 2017.

%H M. Kreuzer, <a href="http://hep.itp.tuwien.ac.at/~kreuzer/CY/CYcy.html">Reflexive polyhedra in 4 dimensions</a>

%H M. Kreuzer and H. Skarke, <a href="http://arXiv.org/abs/hep-th/0002240">Complete classification of reflexive polyhedra in four dimensions</a>, arXiv:hep-th/0002240, 2000.

%H J. C. Lagarias and G. M. Ziegler, <a href="http://dx.doi.org/10.4153/CJM-1991-058-4">Bounds for lattice polytopes containing a fixed number of interior points in a sublattice</a>, Canad. J. Math. 43(1991), 1022-1035.

%H Luca Terzio Pontiggia, <a href="http://wiredspace.wits.ac.za/handle/10539/25803">Computational methods in string and field theory</a>, doctoral dissertation, Univ. of the Witwatersrand, Johannesburg, 2018.

%H A. Tsuchiya, <a href="http://arxiv.org/abs/1411.2122">The delta-vectors of reflexive polytopes and of the dual polytopes</a>, arXiv preprint arXiv:1411.2122 [math.CO], 2014, 2015.

%H G. M. Ziegler, <a href="http://www.mi.fu-berlin.de/math/groups/discgeom/ziegler/Preprintfiles/075PREPRINT.pdf">Questions about polytopes</a>, pp. 1195-1211 of Mathematics Unlimited - 2001 and Beyond, ed. B. Engquist and W. Schmid, Springer-Verlag, 2001.

%Y See A140296 for the regular Fano polytopes.

%K nonn,more

%O 1,2

%A _N. J. A. Sloane_, Jan 21 2004

%E Definition corrected by _Jonathan Sondow_, Dec 08 2012