Seeing His Beatitude's kolpak reminds me of a unique looking liturgical headgear that I saw on videotape of a Byzantine Catholic hierarchical Divine Liturgy that took place in the first years following the collapse of communism in eastern Europe.
The headgear looked like a red koukoulion (no veil) except that it was quite pointed on top with a cross. There was a shine to it that makes me think it was not made of fabric. When I first saw it, I thought the cleric was Armenian. There were two clerics who wore it. I'm not sure whether they were priests or bishops. I have never since that style of headgear since.
Has anyone seen such a liturgical headgear?
Hopefully, my parish library may still have the videotape so that can get another look at it.