by Henk, M., Linke, E., Wills, J. M..
Series: 2009-41, Preprints
Motivated by the problem to improve Minkowski's lower
bound on the successive minima for the class of zonotopes we determine the minimal volume of a zonotope containing the standard crosspolytope. It turns out that this volume can be expressed via the maximal determinant of a 1-matrix, and that in each dimension the set of minimal zonotopes contains a parallelepiped. Based on that link to 1-matrices, we characterize all zonotopes attaining the minimal volume in
dimension 3 and present related results in higher dimensions.
zonotope, successive minima, Hadamard matrices
This paper was published in:
to appear in linear algebra and its applications