Results 11 to 20 of about 19,164 (129)

The maximum number of faces of the Minkowski sum of three convex polytopes

Journal of Computational Geometry, 2015
We derive tight expressions for the maximum number of $k$-faces, $0\le{}k\le{}d-1$, of the Minkowski sum, $P_1+P_2+P_3$, of three $d$-dimensional convex polytopes $P_1$, $P_2$ and $P_3$ in $\mathbb{R}^d$, as a function of the number of vertices of the ...
Menelaos Karavelas, Christos Konaxis, Eleni Tzanaki   +2 more
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The maximum number of faces of the Minkowski sum of three convex polytopes [PDF]

, 2012
We derive tight expressions for the maximum number of $k$-faces, $0\le{}k\le{}d-1$, of the Minkowski sum, $P_1+P_2+P_3$, of three $d$-dimensional convex polytopes $P_1$, $P_2$ and $P_3$ in $\reals^d$, as a function of the number of vertices of the ...
Karavelas, Menelaos I., Konaxis, Christos, Tzanaki, Eleni   +2 more
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Three Theorems, with Computer-Aided Proofs, on Three-Dimensional Faces and Quotients of Polytopes [PDF]

Discrete & Computational Geometry, 2000
The authors prove three theorems: 1. There is a finite list of three-dimensional polytopes such that every rational 9-polytope contains a three-dimensional face in the list. 2. Every nine-dimensional polytope has the three-dimensional simplex as a quotient. 3. Every 5-polytope contains a three-dimensional quotient with at most eight vertices. The proof
Meisinger, G., Kleinschmidt, P., Kalai, G.   +2 more
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Lower bound theorems for general polytopes [PDF]

, 2019
For a $d$-dimensional polytope with $v$ vertices, $d+1\le v\le2d$, we calculate precisely the minimum possible number of $m$-dimensional faces, when $m=1$ or $m\ge0.62d$. This confirms a conjecture of Gr\"unbaum, for these values of $m$. For $v=2d+1$, we
Pineda-Villavicencio, Guillermo, Ugon, Julien, Yost, David   +2 more
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Primal Dividing and Dual Pruning: Output-Sensitive Construction of Four-Dimensional Polytopes and Three-Dimensional Voronoi Diagrams [PDF]

Discrete & Computational Geometry, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chan, T. M., Snoeyink, J., Yap, Chee-Keng   +2 more
openaire   +1 more source

Geometric transition from hyperbolic to Anti-de Sitter structures in dimension four

, 2020
We provide the first examples of geometric transition from hyperbolic to Anti-de Sitter structures in dimension four, in a fashion similar to Danciger's three-dimensional examples.
Riolo, Stefano, Seppi, Andrea
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Few smooth d-polytopes with n lattice points [PDF]

, 2013
We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system.
A. Lundman, A. M. Kasprzyk, A. M. Kasprzyk, A. M. Kasprzyk, Andreas Paffenholz, B. Nill, Benjamin Lorenz, Benjamin Nill, C. Haase, Christian Haase, D. A. Cox, D. Hensley, E. Gawrilow, Francisco Santos, G. A. Pick, G. Ewald, G. M. Ziegler, Günter Rote, H. Sato, Hal Schenck, I. Bárány, J. A. Loera De, J. C. Lagarias, J. E. Reeve, J. Gubeladze, M. Hochster, M. Joswig, M. Kreuzer, M. Kreuzer, M. Kreuzer, Milena Hering, Mini-workshop, O. Pikhurko, P. Kleinschmidt, R. Laterveer, R. P. Stanley, S. Ogata, T. Hibi, T. Oda, Tristram Bogart, V. E. Voskresenskiĭ, V. V. Batyrev, V. V. Batyrev, V. V. Batyrev, W. Bruns, W. Bruns, W. Fulton   +46 more
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Gorenstein toric Fano varieties [PDF]

, 2004
We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry.
Avram, Batyrev, Batyrev, Batyrev, Batyrev, Benjamin Nill, Casagrande, Casagrande, Conrads, Dais, Ewald, Kantor, Kreuzer, Kreuzer, Kreuzer, Kreuzer, Lagarias, Sato, Stillwell, Voskresenskij, Watanabe   +20 more
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Linear Toric Fibrations [PDF]

, 2013
These notes are based on three lectures given at the 2013 CIME/CIRM summer school. The purpose of this series of lectures is to introduce the notion of a toric fibration and to give its geometrical and combinatorial characterizations.
A. Dickenstein, A. Dickenstein, C. Casagrande, C. Haase, G. Ewald, L. Ein, M. Beltrametti, M. Mustata, O. Debarre, S. Rocco Di, S. Rocco Di, T. Oda, V.V. Batyrev   +12 more
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Some Properties of Metric Polytope Constraints

Моделирование и анализ информационных систем, 2014
The integrality recognition problem is considered on the sequence Mn,k of the nested Boolean quadric polytope relaxations, including the rooted semimetric Mn and the metric Mn,3 polytopes.
V. A. Bondarenko, A. V. Nikolaev
doaj   +1 more source