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Is there a deeper meaning for the depiction of Jesus' head tilted towards his right on the Crucifix?
Artists almost universally appear to have agreed to place the soldier’s wound on Christ’s right side and Christ’s head leaning to the right.
Only St. John mentions Jesus’ head in his Gospel account, “bowing his head, he gave up his spirit” (Jn 19:30). Because we cannot determine the actual position of Jesus’ head when he died, artists have exercised some freedom when representing this aspect of the Crucified Christ.
That artists represent Christ’s head leaning to the right may reflect no more than a sensibility that the right is the more noble side. Or the artist may simply wish Christ’s head to echo the position of his wound. - Christ’s Head On the Cross
One could make the argument that Jesus was showing us to turn the other cheek. But we must remember that these are artistic renderings of the Crucifixion of Jesus, by individuals who have never witnessed a crucifixion.
Modern research now has shown that a crucified individual actually dies with his head hung straight down, neither tilted to the right nor to the left.
Shroud of Turin Villandre Crucifix
This has been borne out by Dr. Pierre Barbet in his book, A Doctor at Calvary. It is not for the faint hearted. The Shroud of Turin also bares this out.
Some churches, especially larger Medieval Latin Rite churches were architecturally designed in the form of a cross and some even had the sanctuary area tilted to the right in honour of Christ’s Crucifixion.
The Abbey of Fontgombault is just one example. Having personally been in this church abbey, it is quite obvious., but photos on the net do not do justice to this architectural feature.