منابع مشابه
Valuations and Tensor Weights on Polytopes
Let V be a finite-dimensional vector space over a square-root closed ordered field F (this restriction permits an inner product with corresponding norm to be imposed on V). Many properties of the family P :1⁄4 PðVÞ of convex polytopes in V can be expressed in terms of valuations (or finitely additive measures). Valuations such as volume, surface area and the Euler characteristic are translation...
متن کاملMonotone paths on polytopes
We investigate the vertex-connectivity of the graph of f -monotone paths on a d-polytope P with respect to a generic functional f . The third author has conjectured that this graph is always (d − 1)-connected. We resolve this conjecture positively for simple polytopes and show that the graph is 2-connected for any d-polytope with d ≥ 3. However, we disprove the conjecture in general by exhibiti...
متن کاملOn Some Polytopes
In this paper, we consider polytopes P that are contained in the unit hypercube. We provide conditions on the set of infeasible 0,1 vectors that guarantee that P has a small Chvátal rank. Our conditions are in terms of the subgraph induced by these infeasible 0,1 vertices in the skeleton graph of the unit hypercube. In particular, we show that when this subgraph contains no 4-cycle, the Chvátal...
متن کاملNon-Flat Regular Polytopes and Restrictions on Chiral Polytopes
An abstract polytope is flat if every facet is incident on every vertex. In this paper, we prove that no chiral polytope has flat finite regular facets and finite regular vertex-figures. We then determine the three smallest non-flat regular polytopes in each rank, and use this to show that for n > 8, a chiral n-polytope has at least 48(n− 2)(n− 2)! flags.
متن کاملOn Perfect 4-Polytopes
The concept of perfection of a polytope was introduced by S. A. Robertson. Intuitively speaking, a polytope P is perfect if and only if it cannot be deformed to a polytope of different shape without changing the action of its symmetry group G(P ) on its face-lattice F (P ). By Rostami’s conjecture, the perfect 4-polytopes form a particular set of Wythoffian polytopes. In the present paper first...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1996
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02711515