Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 37 (1996), No. 1, 199-207.

On Maximal Primitive Fixing Systems

Vladimir Boltyanski and Horst Martini

Abstract.

Let $\rho_{\max } (M)$ denote the maximal number of points forming
a primitive fixing system for a convex body $M \subset {\bf R}^n$. 
Sharpening results of B.~Bollob\'as with respect to the quantity
$\rho_{\max } (M)$ for $n \ge 3$, we construct counterexamples to
the conjecture $\rho_{\max } (M) \le 2 (2^n-1)$ of L.~Danzer. These
counterexamples $M$ satisfy $\rho_{\max } (M) = \infty$, and they 
can belong
to the following classes of convex bodies: cap bodies, zonoids,
and zonotopes.\par}

MSC 1991: 52A20