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Enumeration of the quasisimplicial 3-spheres and 4-polytopes with eight vertices

Amos Altshuler, Leon Steinberg

Pacific Journal of Mathematics · 1984 · 36 citations · 27 references

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Abstract

A complete enumeration is given for quasisimplicial 3-spheres with eight vertices. It is found that there are 661 spheres, and it is proved that precisely 20 of these are not polytopal.

References

27

Spaces determined by point-countable covers

Gary Gruenhage, Ernest Michael, Yoshio Tanaka · Pacific Journal of Mathematics · 1984 · 156 citations · Full text

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An enumeration of simplicial 4-polytopes with 8 vertices

Branko Grünbaum, V. P. Sreedharan · Journal of Combinatorial Theory · 1967 · 131 citations

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Shellings of spheres and polytopes

Gopal Danaraj, Victor Klee · Duke Mathematical Journal · 1974 · 109 citations

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The classification of simplicial 3-spheres with nine vertices into polytopes and nonpolytopes

Amos Altshuler, Jürgen Bokowski, Leon Steinberg · Discrete Mathematics · 1980 · 59 citations

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The triangulations of the 3-sphere with up to 8 vertices

David Barnette · Journal of Combinatorial Theory Series A · 1973 · 56 citations

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