"I assume the one on the left is the Father? Is there any significance that Christ and the Spirit have their heads tilted more downward than the Father?"
Here's a Russian interpretation of the Icon:
"All scholars agree that the three hypostases of the Trinity are represented in Rublev's icon. But there are greatly differing views as to which angel represents which hypostasis. Many see Christ in the middle angel and God the Father in the left. Others see God the Father in the middle angel, and Christ in the left one. The middle angel occupies a special place in the icon: it is set apart not only by its central position, but also by a "regal" turn of its head towards the left angel, and by pointing with its hand towards the cup on the table. Both the turn of the head and the gesture are important clues to the hidden meaning of the icon. Equal among equals, the middle angel has such expressive power that one hesitates not to see in it a symbolic representation of God the Father. On the other hand one cannot fail to notice that the left angel is also essential: two other angels lower their heads towards it and seem to address it. Therefore, if we assume that the left angel is God the Father, the middle angel, dressed in the clothes customarily used in compositions depicting the second person of the Trinity (a blue himation and a crimson tunic), should represent Christ. This amazing and perhaps purposeful encoding of these two persons of the Trinity by Rublev does not give us a clear clue for a single interpretation. Whatever the case, the icon shows a dialogue between two angels: The Father turns to His Son and explains the necessity of His sacrifice, and the Son answers by agreeing with His Father's wish.
Neither of these interpretations impacts the interpretation of the Trinity as triune God and as a representation of the sacrament of the Eucharist. The cup on the table is a eucharistic symbol. In the cup we see the head of the calf which Abraham used for the feast. The church interprets this calf as a prototype of the New Testament Lamb, and thus the cup acquires its Eucharistic meaning. The left and the middle angels bless the cup: The Father blesses His Son on his Deed, on His death on the cross for the sake of man's salvation, and the Son, blessing the cup, expresses his readiness to sacrifice Himself. The third angel does not bless the cup and does not participate in the conversation, but is present as a Comforter, the undying, a symbol of eternal youth and the upcoming Resurrection."
About all I can say about typology is that The Church has pointed out these things since the very beginning.
I was able to see some of rublev's icons in Moscow and in Vladimir-Suzdal last september.
But there are greatly differing views as to which angel represents which hypostasis.
Cool. I was sure I was supposed to be able to figure it out, but couldn't. :)
The middle angel occupies a special place in the icon: it is set apart not only by its central position, but also by a "regal" turn of its head towards the left angel, and by pointing with its hand towards the cup on the table.
That's interesting. Why is an angel referred to as "it"?
This amazing and perhaps purposeful encoding of these two persons of the Trinity by Rublev does not give us a clear clue for a single interpretation.
Well, for the interpretations offered, I at least feel good that mine was somewhere in the ballpark. :)
The third angel does not bless the cup and does not participate in the conversation, but is present as a Comforter, the undying, a symbol of eternal youth and the upcoming Resurrection.
However, I did not recognize that the angel on the right was not included in a conversation. Oh well, I'm still in class. :)