Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 37 (1996), No. 1, 41-49.
Redundance of Vertices of the Cube relatively to its Minimal Ellipsoid
Olaf Sarges
Abstract
Each convex body $K$ has a unique ellipsoid of minimal volume
containing $K$ ({\it Minimal ellipsoid, Loewner ellipsoid}).
In this paper we look for subsets of
the vertex set of the cube, which have the same minimal ellipsoid as the cube
itself. All subsets with this property are determined
in dimensions 2,3 and 4.
For some higher dimensions
(for example 4 to 423) we present the minimal cardinal number of such
subsets.
MSC 1991: 52B12, 52A20, 90C34