But perhaps these declarations may seem to have less weight with those who wish to be instructed in divine things out of the holy Scriptures, and who seek to have it proved to them from that source how the nature of God surpasses the nature of bodies. See, therefore, if the apostle does not say the same thing, when, speaking of Christ, he declares, that “He is the image of the invisible God, the first-born of every creature.” Not, as some suppose, that the nature of God is visible to some and invisible to others: for the apostle does not say “the image of God invisible” to men or “invisible” to sinners, but with unvarying constancy pronounces on the nature of God in these words: “the image of the invisible God.” Moreover, John, in his Gospel, when asserting that “no one has seen God at any time,” manifestly declares to all who are capable of understanding, that there is no nature to which God is visible: not as if, He were a being who was visible by nature, and merely escaped or baffled the view of a frailer creature, but because by the nature of His being it is impossible for Him to be seen. (Book I, Part 8)

From the thirty-third chapter, verses 18-23, of Exodus:

Then Moses said, “Now show me your glory.”

And the LORD said, “I will cause all my goodness to pass in front of you, and I will proclaim my name, the LORD, in your presence. I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion. But,” he said, “you cannot see my face, for no one may see me and live.”

Then the LORD said, “There is a place near me where you may stand on a rock. When my glory passes by, I will put you in a cleft in the rock and cover you with my hand until I have passed by. Then I will remove my hand and you will see my back; but my face must not be seen.”

Sounds like a body to me, no matter how awesome and even terrible to behold.

God not having a body is, I think, mostly a matter of neo-Platonic partisanship and disdain for the body. Origen has not convinced me.