Flag vectors of multiplicial polytopes.
Bayer, Margaret M. (2004)
The Electronic Journal of Combinatorics [electronic only]
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Displaying similar documents to “Vertex-vectors of quadrangular 3-polytopes with two types of edges”
Flag vectors of multiplicial polytopes.
Gaps in the Numbers of Vertices of Cubical Polytopes, I.
R. Blind, G. Blind (1994)
Discrete & computational geometry
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On non-inscribable polytopes
Branko Grünbaum, Ernest Jucovič (1974)
Czechoslovak Mathematical Journal
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The Cubical d-Polytopes with Fewer than 2d+1 Vertices.
R. Blind, G. Blind (1995)
Discrete & computational geometry
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All Tight Descriptions of 3-Stars in 3-Polytopes with Girth 5
Oleg V. Borodin, Anna O. Ivanova (2017)
Discussiones Mathematicae Graph Theory
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Lebesgue (1940) proved that every 3-polytope P5 of girth 5 has a path of three vertices of degree 3. Madaras (2004) refined this by showing that every P5 has a 3-vertex with two 3-neighbors and the third neighbor of degree at most 4. This description of 3-stars in P5s is tight in the sense that no its parameter can be strengthened due to the dodecahedron combined with the existence of a P5 in which every 3-vertex has a 4-neighbor. We give another tight description of 3-stars in P5s:...
The lonely vertex problem.
Frettlöh, D., Glazyrin, A. (2009)
Beiträge zur Algebra und Geometrie
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Simple Vertices of Maximal Minor Polytopes
Prakash Santhanakrishnan, Andrei Zelevinsky (1994)
Discrete & computational geometry
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An extension of Kotzig’s theorem on the minimum weight of edges in -polytopes
Oleg V. Borodin (1992)
Mathematica Slovaca
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On the monotone upper bound problem.
Pfeifle, Julian, Ziegler, Günter M. (2004)
Experimental Mathematics
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Rigidity and flexibility of virtual polytopes
G. Panina (2003)
Open Mathematics
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All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.