On Point Sets fixing a Convex Body from within

: We study the concept of a set fixing a convex body from within that was recently proposed by V. Soltan. We prove his conjecture that a finite set which fixes a d-dimensional convex body from within contains a subset of at most 2d points with the same property. 1. Introduction The classical definition [2],[4] of a set S fixing a convex body K ae R d is that S ae K and for each translation by a vector t 2 R d , t 6= 0 there is a point s 2 S and an " ? 0 such that s = 2 interior K but s 2 interior(K + "t). This models a solid object K which is held in its place (against translations) by some points S outside K which would have to move inside K if one tried to force a movement. At the 1995 Intuitive Geometry Conference, V. Soltan defined a new concept of a fixing set. He calls a set S fixing the convex body K ae R d from within if S ae K and for each translation t 6= 0 there is an s 2 S such that s = 2 K + t. This models a rigid surface @K held in its place by some points S insi..