منابع مشابه
Finite polytopes have finite regular covers
We prove that any finite, abstract n-polytope is covered by a finite, abstract regular n-polytope.
متن کاملMubs, Polytopes, and Finite Geometries
A complete set of N + 1 mutually unbiased bases (MUBs) exists in Hilbert spaces of dimension N = p, where p is a prime number. They mesh naturally with finite affine planes of order N , that exist when N = p. The existence of MUBs for other values of N is an open question, and the same is true for finite affine planes. I explore the question whether the existence of complete sets of MUBs is dir...
متن کاملSimple Polytopes Arising From Finite Graphs
Let G be a finite graph allowing loops, having no multiple edge and no isolated vertex. We associate G with the edge polytope PG and the toric ideal IG. By classifying graphs whose edge polytope is simple, it is proved that the toric ideals IG of G possesses a quadratic Gröbner basis if the edge polytope PG of G is simple. It is also shown that, for a finite graph G, the edge polytope is simple...
متن کاملSymmetry Type Graphs of Polytopes and Maniplexes
A k-orbit maniplex is one that has k orbits of flags under the action of its automorphism group. In this paper we extend the notion of symmetry type graphs of maps to that of maniplexes and polytopes and make use of them to study k-orbit maniplexes, as well as fully-transitive 3-maniplexes. In particular, we show that there are no fully-transtive korbit 3-mainplexes with k > 1 an odd number, we...
متن کاملPolytopes with groups of type PGL2(q)
There exists just one regular polytope of rank larger than 3 whose full automorphism group is a projective general linear group PGL2(q), for some prime-power q. This polytope is the 4-simplex and the corresponding group is PGL2(5) ∼= S5.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00339-8