The early Church was faced with many different interpretations, and proceeded to condemn most of them as heresies. Finally the Athanasian Creed clearly stated the symmetry of the Trinity, which was graphically shown in the Shield of the Trinity.

The Church referred to Aristotle more, because he wrote far more clearly than Plato. Aristotle expanded Plato's tripartite classification into 10 categories of being. Later theologians then had to take the time to reduce them down to three again.

I have started a complementary discussion at Arktos, because their focus includes archeology:
Plato's History: From the Bolling warming to the present