Uh, actually I'm looking at a photo of a sample x10 (ex Frank McCrone: Judgement Day for the Shroud of Turin) and does look like a twill - but definitely it is not a herringbone twill.
I believe it -- herringbone twill was a very, very common weave at the time. The various twills were more common than plain-weave, if I am recalling correctly.
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