A090045 Number of equivalence classes of reflexive polytopes in dimension n.

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

Table of n, a(n) for n=1..4.

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, Reflexive polyhedra in 4 dimensions

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

Adjacent sequences: A090042 A090043 A090044 * A090046 A090047 A090048

Keyword

nonn,more

Author

N. J. A. Sloane, Jan 21 2004

Extensions

Definition corrected by Jonathan Sondow, Dec 08 2012

Status

approved