“ Polytope Projections ” ( Discrete Geometry
نویسنده
چکیده
منابع مشابه
Reconstruction of Convex Bodies from Brightness Functions
Algorithms are given for reconstructing an approximation to an unknown convex body from finitely many values of its brightness function, the function giving the volumes of its projections onto hyperplanes. One of these algorithms constructs a convex polytope with less than a prescribed number of facets, while the others do not restrict the number of facets. Convergence of the polytopes to the b...
متن کاملThe Contact Polytope of the Leech Lattice
The contact polytope of a lattice is the convex hull of its shortest vectors. In this paper we classify the facets of the contact polytope of the Leech lattice up to symmetry. There are 1,197,362,269,604,214,277,200 many facets in 232 orbits.
متن کاملPolytopes of Minimum Positive Semidefinite Rank
The positive semidefinite (psd) rank of a polytope is the smallest k for which the cone of k × k real symmetric psd matrices admits an affine slice that projects onto the polytope. In this paper we show that the psd rank of a polytope is at least the dimension of the polytope plus one, and we characterize those polytopes whose psd rank equals this lower bound.
متن کاملDecomposing the Secondary Cayley Polytope
The vertices of the secondary polytope of a point connguration correspond to its regular triangulations. The Cayley trick links triangulations of one point connguration, called the Cayley polytope, to the ne mixed subdivisions of a tuple of point conngurations. In this paper we investigate the secondary polytope of this Cayley polytope. Its vertices correspond to all regular mixed subdivisions ...
متن کاملExtremal Properties of 0/1-Polytopes
We provide lower and upper bounds for the maximal number of facets of a d-dimensional 0/1-polytope, and for the maximal number of vertices that can appear in a two-dimensional projection (“shadow”) of such a polytope.
متن کامل