Displaying similar documents to “Gosset polytopes in integral octonions”

On the refinements of a polyhedral subdivision.

Francisco Santos (2001)

Collectanea Mathematica

Similarity:

Let pi: P --> Q be an affine projection map between two polytopes P and Q. Billera and Sturmfels introduced in 1992 the concept of polyhedral subdivisions of Q induced by pi (or pi-induced) and the fiber polytope of the projection: a polytope Sygma(P,pi) of dimension dim(P)-dim(Q) whose faces are in correspondence with the coherent pi-induced subdivisions (or pi-coherent subdivisions). In this paper we investigate the structure of the poset of pi-induced refinements of a pi-induced...

Uniform decompositions of polytopes

Daniel Berend, Luba Bromberg (2006)

Applicationes Mathematicae

Similarity:

We design a method of decomposing convex polytopes into simpler polytopes. This decomposition yields a way of calculating exactly the volume of the polytope, or, more generally, multiple integrals over the polytope, which is equivalent to the way suggested in Schechter, based on Fourier-Motzkin elimination (Schrijver). Our method is applicable for finding uniform decompositions of certain natural families of polytopes. Moreover, this allows us to find algorithmically an analytic expression...

Approximation of the Euclidean ball by polytopes

Monika Ludwig, Carsten Schütt, Elisabeth Werner (2006)

Studia Mathematica

Similarity:

There is a constant c such that for every n ∈ ℕ, there is an Nₙ so that for every N≥ Nₙ there is a polytope P in ℝⁿ with N vertices and v o l ₙ ( B ₂ ⁿ △ P ) ≤ c v o l ₙ ( B ₂ ⁿ ) N - 2 / ( n - 1 ) where B₂ⁿ denotes the Euclidean unit ball of dimension n.

Rigidity and flexibility of virtual polytopes

G. Panina (2003)

Open Mathematics

Similarity:

All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.