Inscribing a regular octahedron into polytopes

Random inscribing polytopes

For convex bodies K with C2 boundary in Rd, we explore random polytopes with vertices chosen along the boundary of K. In particular, we determine asymptotic properties of the volume of these random polytopes. We provide results concerning the variance and higher moments of this functional, as well as an analogous central limit theorem.

An Inscribing Model for Random Polytopes

For convex bodies K with C2 boundary in Rd, we explore random polytopes with vertices chosen along the boundary of K. In particular, we determine asymptotic properties of the volume of these random polytopes. We provide results concerning the variance and higher moments of this functional, as well as an analogous central limit theorem.

Inscribing a regularm-gon in a regular n-gon

We find necessary and sufficient conditions on m and n for inscribing a regular m-gon in a regular n-gon. Mathematics Subject Classification (2010). Primary 51M20; Secondary 52C15.

On Inscribing «-dimensional Sets in a Regular »-simplex

High-Dimensional Centrally Symmetric Polytopes with Neighborliness Proportional to Dimension

Let A be a d by n matrix, d < n. Let C be the regular cross polytope (octahedron) in R. It has recently been shown that properties of the centrosymmetric polytope P = AC are of interest for finding sparse solutions to the underdetermined system of equations y = Ax; [9]. In particular, it is valuable to know that P is centrally k-neighborly. We study the face numbers of randomly-projected cross-...