Why does every depiction of the face of Jesus Christ produced since circa the 800s look more or less the same?
Uhh...hello...it’s the precise shroud in question.
They don’t. They differ in one important characteristic. Most of them depict Jesus with nails driven through his hands.
A strong piece of evidence for the authenticity of the Shroud is that it doesn’t match the conventional depiction of the post-800 era. The wounds are in the wrists, not the hands — because that would have been the only way for the nails to support the weight of a man’s body on a cross.
Why does every depiction of the face of Jesus Christ produced since circa the 800s look more or less the same?
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Because they copied each other. Common tradition in Holy paintings.