  We introduce an algorithm that embeds a given 3-connected planar graph as a
convex 3-polytope with integer coordinates. The size of the coordinates is
bounded by $O(2^{7.55n})=O(188^{n})$. If the graph contains a triangle we can
bound the integer coordinates by $O(2^{4.82n})$. If the graph contains a
quadrilateral we can bound the integer coordinates by $O(2^{5.46n})$. The
crucial part of the algorithm is to find a convex plane embedding whose edges
can be weighted such that the sum of the weighted edges, seen as vectors,
cancel at every point. It is well known that this can be guaranteed for the
interior vertices by applying a technique of Tutte. We show how to extend
Tutte's ideas to construct a plane embedding where the weighted vector sums
cancel also on the vertices of the boundary face.
