The characterization and the canonical representation of order-n phase type distributions (PH(n)) is an open research problem.This problem is solved for n = 2, since the equivalence of the acyclic and the general PH distributions has been proven for a long time. However, no canonical representations have been introduced for the general PH distribution class so far for n > 2. In this paper we summarize the related results for n = 3. Starting from these results we provide a canonical representation of the PH(3) class (that is a minimal representation, too) and present a symbolical transformation procedure to obtain the canonical representation based on any (not only Markovian) vectormatrix representation of the distribution. We show that -using the same approachno symbolical results can be derived for the order-4 PH distributions, thus probably the PH(3) class is the highest order PH class for which a symbolical canonical transformation exists.Using the transformation method to canonical form for PH(3) we numerically evaluate the moment bounds of the PH(3) distribution set, compare it to the order-3 acyclic PH distribution (APH(3)) class, and present other possible applications of the canonical form.Email address: {ghorvath,telek}@hit.bme.hu (Gábor Horváth and Miklós Telek).