A133338 Number of combinatorial types of neighborly 4-polytopes with n vertices.

1, 1, 1, 3, 23, 431, 13935, 556062

Offset

5,4

References

B. Gruenbaum, Convex Polytopes, 2nd Edition, p. 129a.

Links

Table of n, a(n) for n=5..12.

Djordje Baralić and Lazar Milenković, Surprising Examples of Manifolds in Toric Topology!, arXiv:1704.05932 [math.AT], 2017.

Djordje Baralić and Lazar Milenković, Small Covers and Quasitoric Manifolds over Neighborly Polytopes, Mediterr. J. Math. 19, 87 (2022).

Moritz Firsching, Realizability and inscribability for simplicial polytopes via nonlinear optimization, arXiv:1508.02531 [math.MG], 2015.

Firsching, Moritz Realizability and inscribability for simplicial polytopes via nonlinear optimization. Math. Program. 166, No. 1-2 (A), 273-295 (2017). Table 1

Moritz Firsching, The complete enumeration of 4-polytopes and 3-spheres with nine vertices, arXiv:1803.05205 [math.MG], 2018.

Moritz Firsching, Classifications and realizations; alternative link

Crossrefs

Cf. A005841, A222318.

Sequence in context: A118195 A055326 A271851 * A298466 A358069 A116986

Adjacent sequences: A133335 A133336 A133337 * A133339 A133340 A133341

Keyword

nonn,more

Author

Gabriel Cunningham (oeis(AT)gabrielcunningham.com), Oct 19 2007

Extensions

a(11)-a(12) from Moritz Firsching's page added by Andrey Zabolotskiy, Dec 24 2021

a(12) corrected from 556061 to 556062 based on Baralić & Milenković's paper. Apparently earlier I misinterpreted Firsching's data. - Andrey Zabolotskiy, Aug 27 2022

Status

approved