Bets,
yes it would in any case come to distortions for geometrical reasons. If the cover would be flat like a plane, then only the top of the nose will cause a dot. If it is wrapped tightly, there would be an entire imprint, but when you unwrap it again, it will look quite strange. Check it out practically and you will know what I mean. It's the same principle to try to make a flat map of the round earth, it's impossible without distortions.

Personally, I like the theory that Leonardo Da Vinci fabricated the shroud.

Spooky