Is this 3-over-1 twill?  Is this a different fragment or the other side? Gian Marco Rinaldi tells us this is the warp side.  Also look at the two pictures shown below as well from the 11:31 mark in the video at:

http://www.statemuseum.arizona.edu/podcasts/ep033_beyond_naked_eye.shtml

We need a better understanding of this.

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