  For a sum of squares domain of finite D'Angelo 1-type at the origin, we show
that the polynomial model obtained from the computation of the Catlin multitype
at the origin of such a domain is likewise a sum of squares domain. We also
prove, under the same finite type assumption, that the multitype is an
invariant of the ideal of holomorphic functions defining the domain. Both
results are proven using Martin Kolar's algorithm for the computation of the
multitype introduced in [13]. Given a sum of squares domain, we rewrite the
Kolar algorithm in terms of ideals of holomorphic functions and also introduce
an approach that explicitly constructs the homogeneous polynomial
transformations used in the algorithm.
