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

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

Offset

5,4

Comments

For one of the 556062 combinatorial types of polytopes with n=12 vertices, it is unknown if it has a geometric realization. - Andrei Zabolotskii, Apr 12 2026

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). See also the accompanying code and data.

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

Moritz Firsching, 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.

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 Andrei Zabolotskii, Dec 24 2021

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

Status

approved