Watch the Nestorianism there, bub.
God the Father it is generally believed does not have a physical body as we know it.
God the Son, however, who is both 100% God and 100% man, did at His incarnation, and does even now, have a physical body.
And God the Holy Spirit does not in general manifestation, except in rare instances where His form seems to take a material shape (a dove, fire, etc.). Nevertheless, His manifestations tend not to be human in the way Christ is.
But if this is a challenge to the orthodox (i.e., biblical) doctrine of the Holy Trinity (as outlined by the Nicene, Apostolic, and Athanasian Creeds), my response is a question for you: who is Jesus' true father? According to the Scriptures, the Holy Spirit is the one who conceived Him. But throughout His life, Jesus claimed that God the Father was. And is the Holy Spirit the Spirit of God the Father or the Spirit of Christ?
The greatest minds in Christendom have from the very beginning tried to understand these things. Within the limitations of human understanding, it doesn't make sense. But then again, we are talking about the divine nature, something that by its very nature is difficult for humans to understand. What the greatest minds in Christendom concluded is essentially what we call Athanasian or Orthodox Trinitarianism. Three Persons, yet only One God. And the Second of the Three Persons, Christ is both fully God and fully human. To propose that we are speaking of multiple Gods is a discredit to the Bible's clear monotheistic teachings, and to propose that all three Persons are not equally God is to discredit Jesus' own teachings. So even if these things are beyond our understanding, they are clearly the right confession of the Holy Christian Church.
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Shampoo, the idea of God having three heads is essentially an analogy attempting to explain how the Three Persons are only One God - distinct, yet the same. All analogies are imperfect, however, as we can only conceive of those things within the limits of our own existence.
Oh, and as for the possibility of Jesus' physical body being in multiple places at once: the Scriptures teach that, in the Sacrament, Jesus' body and blood are indeed present in the forms of bread and wine, to the degree that partaking in an unbelieving disposition is actually a sin against His body and blood (1 Corinthians 11:27-29). So somehow, as both God and Man, he is able to accomplish it. But remember, this is the same God-Man who fed several thousand people with only two tiny fish and five small cakes of bread.