[1]

A. Altshuler, L. Steinberg, Enumeration of the quasisimplicial 3-spheres and 4-polytopes with eight vertices. *Pacific J. Math.* 113 (1984), 269–288. MR749536 Zbl 0512.52004Google Scholar

[2]

A. Altshuler, L. Steinberg, The complete enumeration of the 4-polytopes and 3-spheres with eight vertices. *Pacific J. Math.* 117 (1985), 1–16. MR777434 Zbl 0512.52003Google Scholar

[3]

E. K. Babson, C. S. Chan, Counting faces of cubical spheres modulo two. *Discrete Math.* 212 (2000), 169–183. MR1748648 Zbl 0947.52004Google Scholar

[4]

D. Barnette, The projection of the *f*-vectors of 4-polytopes onto the(*E*, *S*)-plane. *Discrete Math.* 10 (1974), 201–216. MR0353148 Zbl 0294.52008Google Scholar

[5]

D. Barnette, J. R. Reay, Projections of *f*-vectors of four-polytopes. *J. Combin. Theory Ser. A* 15 (1973), 200–209. MR0320890 Zbl 0263.05030Google Scholar

[6]

M. M. Bayer, L. J. Billera, Generalized Dehn-Sommerville relations for polytopes, spheres and Eulerian partially ordered sets. *Invent. Math.* 79 (1985), 143–157. MR774533 Zbl 0543.52007Google Scholar

[7]

M. M. Bayer, C. W. Lee, Combinatorial aspects of convex polytopes. In: *Handbook of convex geometry, Vol. A, B*, 485–534, North-Holland 1993. MR1242988 Zbl 0789.52014Google Scholar

[8]

A. Björner, Face numbers of complexes and polytopes. In: *Proceedings of the International Congress of Mathematicians, Vol.* 1, 2 (*Berkeley, Calif.,* 1986), 1408–1418, Amer. Math. Soc. 1987. MR934345 Zbl 0672.52005Google Scholar

[9]

A. Björner, Partial unimodality for *f*-vectors of simplicial polytopes and spheres. In: *Jerusalem combinatorics ‘*93, volume 178 of *Contemp. Math.*, 45–54, Amer. Math. Soc. 1994. MR1310573 Zbl 0815.52011Google Scholar

[10]

A. Björner, S. Linusson, The number of *k*-faces of a simple *d*-polytope. *Discrete Comput. Geom.* 21 (1999), 1–16. MR1661283 Zbl 0935.52010Google Scholar

[11]

G. Blind, R. Blind, Gaps in the numbers of vertices of cubical polytopes. I. *Discrete Comput. Geom.* 11 (1994), 351–356. MR1271640 Zbl 0807.52009Google Scholar

[12]

P. Brinkmann, G. M. Ziegler, Small *f*-vectors of 3-spheres and of 4-polytopes. *Math. Comp.* 87 (2018), 2955–2975. MR3834694 Zbl 06912364Google Scholar

[13]

W. Bruns, J. Gubeladze, N. V. Trung, Problems and algorithms for affine semigroups. *Semigroup Forum* 64 (2002), 180–212. MR1876854 Zbl 1018.20048Google Scholar

[14]

J. Eckhoff, Combinatorial properties of *f*-vectors of convex polytopes. Unpublished manuscript, Dortmund 1985.Google Scholar

[15]

J. Eckhoff, Combinatorial properties of *f*-vectors of convex polytopes. *Normat* 54 (2006), 146–159. MR2288936Google Scholar

[16]

B. Grünbaum, *Convex polytopes*. Springer 2003. MR1976856 Zbl 1024.52001Google Scholar

[17]

M. Henk, J. Richter-Gebert, G. M. Ziegler, Basic properties of convex polytopes. In: *Handbook of discrete and computational geometry*, 383–413, CRC, Boca Raton, FL 2017. MR1730169 Zbl 0911.52007Google Scholar

[18]

W. Höhn, *Winkel und Winkelsumme im n-dimensionalen euklidischen Simplex*. Thesis, Eidgenössische Technische Hochschule Zürich 1953. MR0056299Google Scholar

[19]

A. Höppner, G. M. Ziegler, A census of flag-vectors of 4-polytopes. In: *Polytopes—combinatorics and computation* (*Oberwolfach,* 1997), volume 29 of *DMV Sem.*, 105–110, Birkhäuser 2000. MR1785294 Zbl 0966.52008Google Scholar

[20]

G. Kalai, Rigidity and the lower bound theorem. I. *Invent. Math.* 88 (1987), 125–151. MR877009 Zbl 0624.52004Google Scholar

[21]

V. Klee, A combinatorial analogue of Poincaré’s duality theorem. *Canad. J. Math.* 16 (1964), 517–531. MR0189039 Zbl 0134.42403Google Scholar

[22]

T. Kövari, V. T. Sós, P. Turán, On a problem of K. Zarankiewicz. *Colloquium Math.* 3 (1954), 50–57. MR0065617 Zbl 0055.00704Google Scholar

[23]

E. Miller, B. Sturmfels, *Combinatorial commutative algebra*. Springer 2005. MR2110098 Zbl 1090.13001Google Scholar

[24]

H. Sjöberg, G. M. Ziegler, Semi-algebraic sets of *f*-vectors. Preprint, 10 pages, August 2017. arXiv:1711.01864 [math.MG]Google Scholar

[25]

E. Steinitz, Über die Eulerschen Polyederrelationen. *Archiv der Mathematik und Physik* 11 (1906), 86–88. JFM 37.0500.01Google Scholar

[26]

A. Werner, *Linear Constraints on Face Numbers of Polytopes*. PhD thesis, TU Berlin, 2009. iv+185 pages, http://opus.kobv.de/tuberlin/volltexte/2009/2263/Google Scholar

[27]

G. M. Ziegler, *Lectures on polytopes*. Springer 1995. MR1311028 Zbl 0823.52002Google Scholar

[28]

G. M. Ziegler, Face numbers of 4-polytopes and 3-spheres. In: *Proceedings of the International Congress of Mathematicians, Vol. III* (*Beijing,* 2002), 625–634, Higher Ed. Press, Beijing 2002. MR1957565 Zbl 1006.52006Google Scholar

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