  We study three finite-dimensional quotient vector spaces constructed from the
linear span of the set of characteristic functions of permutohedral cones by
imposing two kinds of constraints: (1) neglect characteristic functions of
higher codimension permutohedral cones, and (2) neglect characteristic
functions of non-pointed permutohedral cones. We construct an ordered basis
which is canonical, in the sense that it has subsets which map onto ordered
bases for the quotients. We present straightening relations to the canonical
basis, and using Laplace transforms we obtain functional representations for
each quotient space.
