منابع مشابه
On Gale and braxial polytopes
Cyclic polytopes are characterized as simplicial polytopes satisfying Gale’s evenness condition (a combinatorial condition on facets relative to a fixed ordering of the vertices). Periodically-cyclic polytopes are polytopes for which certain subpolytopes are cyclic. Bisztriczky discovered a class of periodically-cyclic polytopes that also satisfy Gale’s evenness condition. The faces of these po...
متن کاملA Construction for Periodically-Cyclic Gale 2m-Polytopes
For each v, k and m such that v ≥ k ≥ 2m + 2 ≥ 8, we construct a periodically-cyclic Gale 2m-polytope with v vertices and the period k. For such a polytope, there is a complete description of each of its facets based upon a labelling (total ordering) of the vertices so that every subset of k successive vertices generates a cyclic 2m-polytope. MSC 2000: 52B11, 52B05
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 semihypergroups and hypergroups
in this thesis, first the notion of weak mutual associativity (w.m.a.) and the necessary and sufficient condition for a $(l,gamma)$-associated hypersemigroup $(h, ast)$ derived from some family of $lesssim$-preordered semigroups to be a hypergroup, are given. second, by proving the fact that the concrete categories, semihypergroups and hypergroups have not free objects we will introduce t...
15 صفحه اولOn Reduced Polytopes and Antipodality
Let B be an o-symmetric convex body in R, and M be the normed space with unit ball B. The M-thickness ∆B(K) of a convex body K ⊆ R is the smallest possible Mdistance between two distinct parallel supporting hyperplanes of K. Furthermore, K is said to be M-reduced if ∆B(K ′) < ∆B(K) for every convex body K ′ with K ′ ⊆ K and K ′ 6= K. In our main theorems we describe M-reduced polytopes as polyt...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2007
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-007-2163-x