Polytopes and polyhedra - Open Access .click

Results 101 to 110 of about 181 (122)

, 2013
Polytopes may be defined as the convex hull of finitely many points in n-dimensional space ℝ n . They are fundamental objects in computational geometry. When studying polytopes, it soon becomes apparent that the proof of seemingly obvious properties often requires further clarification of the basic underlying geometric structures. An example of this is
Michael Joswig, Thorsten Theobald
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On the p-Median Polytope and the Intersection Property: Polyhedra and Algorithms

SIAM Journal on Discrete Mathematics, 2011
We study a prize-collecting version of the uncapacitated facility location problem and of the $p$-median problem. We say that the uncapacitated facility location polytope has the intersection property if adding the extra equation that fixes the number of opened facilities does not create any fractional extreme point.
Mourad Baı̈ou, Francisco Barahona, José Correa +2 more
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Polygons, Polyhedra, and Polytopes

, 1991
In this chapter, we specialize from general convex sets to convex polygons and polyhedra. Their additional structure leads to many further properties worthy of particular study. Few can fail to appreciate the elegance and symmetry of polyhedral models.
H. T. Croft, K. J. Falconer, Richard K. Guy +2 more
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A Theory of Nets for Polyhedra and Polytopes Related to Incidence Geometries

Designs, Codes and Cryptography, 1997
The authors investigate nets of polyhedra, and their generalizations (also for polytopes and combinatorial polytopes), from the viewpoint of incidence geometry, i.e., in terms of morphisms of geometries and the adjacency graph of faces. One of their main observations is that a great deal of this study only require the combinatorial structure (although ...
Sabine Bouzette +3 more
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Bounding the Numbers of Faces of Polytope Pairs and Simple Polyhedra

, 1984
Let P be a simplicial d -polytope with v vertices and Σ( P ) be the simplicial ( d – 1)-complex associated with the boundary of P . Suppose, for a given face F of P , that we know the numbers of faces of various dimensions of lk Σ( p ) F .
Carl W. Lee
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Symmetry of Polytopes and Polyhedra