Publication

Belt distance between facets of space-filling zonotopes

2012
Journal Articles

Abstract

To every d-dimensional polytope P with centrally symmetric facets one can assign a “subway map” such that every line of this “subway” contains exactly the facets parallel to one of the ridges of P. The belt diameter of P is the maximum number of subway lines one needs to use to get from one facet to another. We prove that the belt diameter of a d-dimensional space-filling zonotope does not exceed ⌈log2(4/5)d⌉.

Official source

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

2012
Journal Articles

Abstract

Official source

Related concepts (15)

Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the -dimensional Euclidean space . Most texts use the term "polytope" for a bounded convex polytope, and the word "polyhedron" for the more general, possibly unbounded object. Others (including this article) allow polytopes to be unbounded. The terms "bounded/unbounded convex polytope" will be used below whenever the boundedness is critical to the discussed issue.

4-polytope

In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure, composed of lower-dimensional polytopal elements: vertices, edges, faces (polygons), and cells (polyhedra). Each face is shared by exactly two cells. The 4-polytopes were discovered by the Swiss mathematician Ludwig Schläfli before 1853. The two-dimensional analogue of a 4-polytope is a polygon, and the three-dimensional analogue is a polyhedron.

Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. All its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are regular polytopes of dimension ≤ n. Regular polytopes are the generalized analog in any number of dimensions of regular polygons (for example, the square or the regular pentagon) and regular polyhedra (for example, the cube).

Related publications (12)

Belt distance between facets of space-filling zonotopes

Chat with Graph Search

Tropical Ehrhart Theory and Tropical Volume

Extended Formulations from Communication Protocols in Output-Efficient Time

On 2-Level Polytopes Arising In Combinatorial Settings