Great Moscow Synod of 1666 forbade depictions of God the Father, themselves a result of Latin influence. But that didn't immediately stop iconographers, and even today, some (often reconstituted) old cathedrals have depictions of God the Father (see >>666462 ).
But modern canonical iconography indeed doesn't permit images of God the Father. It doesn't fit into the theology of Byzantine iconography (simply put, our icon of the New Testament Trinity is the icon of Jesus Himself) and any serious iconographer would reee at stuff like >>666460 (where there is the double whammy of the Holy Spirit being portrayed as a dove outside of the Theophany + God the Father being portrayed).
I'd say that the closest thing to a theologically correct Trinity icon without being strictly canonical is pic related. It portrays the concept of interprenetation, it has "the Father" actually being Jesus as the Ancient of Days (see the halo), and it goes back to the Revelation imagery of God and the Lamb sitting on the throne and the river of life proceeding from both.
But it's still not a good icon of the Trinity.
Why are portrayals of the Father not canonical? Not because of anti-Latin autism as with 99% of Orthodox things, but because it is strict in Byzantine theology that only that what was revealed (whether in observable history or in the scriptures) can be portrayed. The Father obviously never showed up as an old bearded man, and all appearances of God in the OT are of the pre-incarnate Logos. The Father can be "seen" as the Hand of God though (something also done in Jewish iconography), or portraying Jesus as the Ancient of Days can link back to the Father without actually showing Him.