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For a sum of squares domain of finite D'Angelo 1-type at the origin, we showthat the polynomial model obtained from the computation of the Catlin multitypeat the origin of such a domain is likewise a sum of squares domain. We alsoprove, under the same finite type assumption, that the multitype is aninvariant of the ideal of holomorphic functions defining the domain. Bothresults are proven using Martin Kolar's algorithm for the computation of themultitype introduced in [13]. Given a sum of squares domain, we rewrite theKolar algorithm in terms of ideals of holomorphic functions and also introducean approach that explicitly constructs the homogeneous polynomialtransformations used in the algorithm.

On the Catlin multitype of sums of squares domains