Convex polytopes in linear spaces

Convex polytopes and linear algebra

This paper defines, for each convex polytope ∆, a family Hw∆ of vector spaces. The definition uses a combination of linear algebra and combinatorics. When what is called exact calculation holds, the dimension hw∆ of Hw∆ is a linear function of the flag vector f∆. It is expected that the Hw∆ are examples, for toric varieties, of the new topological invariants introduced by the author in Local-gl...

Linear time approximation of 3D convex polytopes

On Convex Topological Linear Spaces.

Introduction. In an earlier article [9] the author developed at some length the theory of certain mathematical objects which he called linear systems. It is the purpose of the present paper to apply this theory to the study of convex topological linear spaces. This application is based on the many-to-one correspondence between convex topological linear spaces and linear systems which may be set...

The symplectic spaces that correspond to nonrational, nonsimple convex polytopes

We construct, for each convex polytope, possibly nonrational and nonsimple, a family of compact spaces that are stratified by quasifolds, i.e. each of these spaces is a collection of quasifolds glued together in an suitable way. A quasifold is a space locally modelled on R k modulo the action of a discrete, possibly infinite, group. The way strata are glued to each other also involves the actio...

Classification of Finite Metric Spaces and Combinatorics of Convex Polytopes

We describe the canonical correspondence between finite metric spaces and symmetric convex polytopes, and formulate the problem about classification of the metric spaces in terms of combinatorial structure of those polytopes.