  For any given sum of squares domain in $\mathbb{C}^n,$ we reduce the
complexity in Catlin's multitype techniques by giving a complete normalization
of the geometry. Using this normalization result, we present a more elementary
proof of the equality of the Catlin multitype and the commutator multitype for
such domains when both invariants are finite. Finally, we reformulate
algebraically Catlin's machinery for the commutator multitype computation at
the origin for any given sum of squares domain in $\mathbb{C}^n$.
