A Good Example for the Trinity?

There have been many attempts to give an analogy to show that the Bible teaches that God is both one being, and yet three persons. Many of them are quite insufficient in their attempts. Many of them erroneously give the impression that the Father is one third God, the Son is one third God, and the Spirit is one third God, as if each were a part of God rather than each being fully God. How can three persons be one person? Well, they can't, and the orthodox doctrine of the Trinity does not say such a thing. 

There are three persons, but only one divine essence or substance or nature. Nor does the orthodox doctrine of the Trinity teach that each person of the Godhead is merely one of the "faces," "personas," or "masks," or "modes" in which the one God appears at different times. That is what is called Modalism or Sabellianism, of which I have written much about through the years. It is true that our word "person," like the word "prosopon" in the Greek new testament, means face, countenance, appearance or person. So we read of "the face (prosopon) of Jesus Christ" (II Cor. 4: 6), which reflects the face of the Father. 

With this being said, let us notice Ezekiel's "four living creatures" and see if they might help us to conceptualize how the Father, the Son, and the Spirit can be one and yet be three persons.

"5 Also from within it came the likeness of four living creatures. And this was their appearance: they had the likeness of a man. 6 Each one had four faces, and each one had four wings. 7 Their legs were straight, and the soles of their feet were like the soles of calves’ feet. They sparkled like the color of burnished bronze. 8 The hands of a man were under their wings on their four sides; and each of the four had faces and wings. 9 Their wings touched one another. The creatures did not turn when they went, but each one went straight forward. 10 As for the likeness of their faces, each had the face of a man; each of the four had the face of a lion on the right side, each of the four had the face of an ox on the left side, and each of the four had the face of an eagle. 11 Thus were their faces." (Ezekiel 1: 5-11 nkjv)

My question is this: was each living creature four beings in one since they each had four faces? My next question is this: does the one God have three faces or persons in a similar way that the living creatures are one creature and yet are four separate or distinct creatures (man, lion, ox, eagle)? 

Penny for your thoughts.