Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 37 (1996), No. 1, 9-15.

Invariante Beleuchtung konvexer K\"orper

Benulf Wei{\ss}bach

Abstract

To each convex body $K$ one can assign an isometrical invariant $L^* (K)$, 
which is the smallest number of directions illuminating the boundaries of all 
congruent copies of $K$. The main result of the present paper is an upper 
bound for $L^* (K)$ if $K$ belongs to the set of bodies of constant width in 
a d-dimensional euclidean space. Besides a proof is given for the assertion 
by M. Lassak that each three-dimensional body of constant width can be 
illuminated by six directions, mutually orthogonal or opposite.

MSC 1991: 52A40