But that is the way the Lord Jesus Christ presents God in John chapter 14 by stating what each of the three persons attributes are.
"My Father's house" (verse 2) indicates the Father owns and has a place for His own.
The Father is glorified in the Son (what the Son does [verse 13].
And the Holy Spirit teaches us all things relating to them [verse 26] .
Each person and role is distinct here. The fact that God is three persons acting in unity is something that must be embraced by faith.
The father is the source. The Son is the executive -- executes the will of the Father. The Holy Ghost is the attitude(s) of the Father as manifested by the Son. They are in agreement, or are One.
Mankind reflects the same triunity. Man has a nature (the source or father of his being) whose personality reveals the type person he is. The same can be said of God. The source of Jesus Christ is the Father, whose personality (Holy Spirit) reveals to mankind The person of Christ, hence, God Himself. "I and my Father are One," said Jesus.
The three aspects together reveal the totality of God in the same way that length times width times height reveals the dimensions of an object and the three limitless directions of space.
Just so I understand what you mean when you use the word, person, are you saying that God sees three of himself when he looks in the mirror or is that just metaphorically speaking?
Perhaps we can use jesus4life's reference to the Godhead as a point of departure here if you want to discuss it further.
The reason I brought it up to begin with was to select a part of jesus4life's scripture that isn't really all that clear to most folks and I believed I had something to offer as well, in that it's a body ministry.