A K-simplex is a convex set
affinely homeomorphic to the positive face of the unit ball of a Kakutani
L-space and an octahedron is a convex set affinely homeomorphic to the entire
unit ball. It is shown how to barycentrically subdivide K-simplexes and
octahedra so that the K-simplexes in the subdivision are affinely homeomorphic
to the simplexes of probability measures on closed subsets of (0,∞) with
the weak topology. As a consequence, for any closed subset C of (0,∞),
an apparently new complete metric for the weak topology on ℳ1+(C) is
given.