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A090045
Number of equivalence classes of reflexive polytopes in dimension n.
2
1, 16, 4319, 473800776
OFFSET
1,2
COMMENTS
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
LINKS
Ross Altman, James Gray, Yang-Hui He, Vishnu Jejjala, Brent D. Nelson. A Calabi-Yau database: threefolds constructed from the Kreuzer-Skarke list, Journal of High Energy Physics, 2015, doi://10.1007/JHEP02(2015)158 .
C. F. Doran and U. A. Whitcher, From polygons to string theory, Math. Mag., 85 (2012), 343-359.
Amihay Hanany and Rak-Kyeong Seong, Brane Tilings and Reflexive Polygons, arXiv:1201.2614 [hep-th], 2012.
YH He, V Jejjala, L Pontiggia, Patterns in Calabi--Yau Distributions, arXiv preprint arXiv:1512.01579 [hep-th], 2015.
Yang-Hui He, Rak-Kyeong Seong, Shing-Tung Yau, Calabi-Yau Volumes and Reflexive Polytopes, arXiv:1704.03462 [hep-th], 2017.
M. Kreuzer and H. Skarke, Complete classification of reflexive polyhedra in four dimensions, arXiv:hep-th/0002240, 2000.
J. C. Lagarias and G. M. Ziegler, Bounds for lattice polytopes containing a fixed number of interior points in a sublattice, Canad. J. Math. 43(1991), 1022-1035.
Luca Terzio Pontiggia, Computational methods in string and field theory, doctoral dissertation, Univ. of the Witwatersrand, Johannesburg, 2018.
A. Tsuchiya, The delta-vectors of reflexive polytopes and of the dual polytopes, arXiv preprint arXiv:1411.2122 [math.CO], 2014, 2015.
G. M. Ziegler, Questions about polytopes, pp. 1195-1211 of Mathematics Unlimited - 2001 and Beyond, ed. B. Engquist and W. Schmid, Springer-Verlag, 2001.
CROSSREFS
See A140296 for the regular Fano polytopes.
Sequence in context: A268757 A272358 A176369 * A201241 A123280 A289904
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Jan 21 2004
EXTENSIONS
Definition corrected by Jonathan Sondow, Dec 08 2012
STATUS
approved