BLASCHKE-DECOMPOSABLE CONVEX-BODIES

For a given centred convex body K of R-n, n greater than or equal to 3 , let H-K be the class of all convex bodies with the same projection b ody as K. The question whether K can be expressed as a Blaschke averag e of two non-homothetic bodies from H-K is considered. Necessary and s ufficient conditions on K to be Blaschke decomposable in H-K are given . The paper provides also a characterization of the bodies K such that the Blaschke indecomposable bodies in H-K are dense in H-K itself.