I was always taught that since only Christ assumed flesh, he can be portrayed on icons, but never God the Father.
Whoever taught you this error must not be a very deep thinker. The Holy Spirit has never assumed flesh, and He is depicted in icons. Angels have no flesh, and yet they are depicted in icons. The argument which says the Father must have taken on flesh in order to be depicted is fallacious and easily refuted.
St. John of Damascus - On the Divine Images, Third Apology:If Holy Scripture clothes God in figures which are apparently material, and can even be seen, they are still immaterial. They were seen by the prophets and those to whom they were revealed, not with bodily but with intellectual eyes. They were not seen by all. In a word it may be said that we can make images of all the forms which we see. We apprehend these as if they were seen.
If it can be seen, it can be depicted. That is why the Holy Spirit and angels are depicted in icons, even though they have never been incarnate. The Father has been seen, so He can be depicted, and that is why images of the Father exist everywhere in the Church.
The Octoechos, Tone 5, Midnight Office Canon to the Holy and Life Creating Trinity, Ode 4, first troparion:"Daniel was initiated into the mystery of the threefold splendour of the one Dominion when he beheld Christ the Judge going unto the Father while the Spirit revealed the vision."
St. Ephraim the Syrian
Select Works of S. Ephrem the Syrian: Volume II p.511For when [God whom we have called] a mirror was incapable of old age, and the (Jewish) people incapable of the truth, He took to Himself old age for the instructing of the faithless: and since king and old man and child were become effeminate, He put on old age; as a venerable old man did He judge those iniquitous persons who were effeminate in sin. The Being that waxeth not old put on old age to teach by parables concerning His Son and His Beloved. By the mask of old age He shewed His Fatherhood to teach that He hath a Son, the Son of Man, Whom Daniel saw standing before the Ancient of Days, Who did away with mortal kings, and made Himself a King in the Son of the King Immortal. If it had been One only that was sitting, then had there been one seat; but for this reason he saw not one seat, but seats. He shewed that there was an Assessor with Him, and a Son to the Ancient of Days.
St. Epiphanius of Cyprus
Panarion Volume III14,3 This Father, Son and Holy Spirit has always vouchsafed to appear in visions to his saints, as each was able to receive [the vision] in accordance with the gift which had been <given> him by the Godhead. This gift was granted to each of those who were deemed worthy, sometimes to see the Father as each was able, <sometimes> to hear his voice as well as he could. (4) When he said by the mouth of Isaiah, “My beloved servant shall understand,” this is the voice of the Father. And when Daniel saw “the Ancient of Days,” this is a vision of the Father. And again, when he says in the prophet, “I have multiplied visions and been portrayed by hands of the prophets,” this is the voice of the Son. And when, in Ezekiel, “The Spirit of God took me” and “brought me out unto the plain,” this refers to the Holy Spirit.