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In the Catholic Church the coffin is carried in feet first, symbolic of the fact that in life, the deceased faced the altar. The coffin is turned around at the end of Mass symbolizing the deceased leaving the church.
In the funeral of a priest, (post Vat II) the wake takes place in the church. At the wake the body is usually parallel to the altar. At the beginning of the Mass the coffin is closed, and rotated with the head pointing towards the altar, for when alive, the priest faced the people. At the end of Mass the coffin is not turned around, as the priest would already be in the proper position to exit the church.