… zonotopes, polar zonotopes, and hyperplane arrangements. … arrangement associated with
the zonotope Πn−1. Following … simplicial complex J of proper faces of the polar zonotope Π∆ …

… zonotopes Minkowski sum is cheap and the intersection of two zonotopes is not generally a
zonotope. … For example, the image of an affine map is cheap for zonotopes and polyhedra in …

… The third route is followed by Koshevoy [34], who suggests the use of the Lorenz zonotope
… – the Lorenz zonotope of the former distribution is included in the Lorenz zonotope of the …

… Zonotopes exhibit special … between zonotopes and hyperplane arrangements is rich,
and includes intriguing connections between the different tilings of the zonotope into sub-zonotopes …

… We prove the second Voronoi conjecture on parallelohedra for zonotopes. We show that
for … copies of a zonotope Z there are d vectors connecting the centers of zonotopes with a …

… of the zonotope, we can find this instance by examining all the vertices of the zonotope of
⃗r(q). To … of ⃗r(q) by examining all the vertices and edges of the zonotope. If the origin is in the …

Let A be an n×N real-valued matrix with n<N; we count the number of k-faces f k (AQ) when
Q is either the standard N-dimensional hypercube I N or else the positive orthant ℝ + N . To …

… sets, called zonotopes, fill a convex cone in the space of compact convex sets, and the cone
of zonotopes is … The zonotopes of the present epoch were called parallelohedra those days. …

… that, for any plane zonotope and the corresponding integer matrix A, we can choose a …
The matrix A determining the given plane zonotope contains two columns and consists of …

This thesis consists of two parts. In the first part, we start by investigating the classical
permutohedra as Minkowski sums of the hypersimplices. Their volumes can be expressed as …