I have some experience with weaving on 2 and 4 harness looms and a traditional diamond weave is just a variation on a twill weaving pattern. As with any basic woven fabric you will have stretch along the basis as the warp and weft fibers slid over each other. WV's fabric appears to be a diamond twill weave. Porkchop's fabric appears to be something different - I would guess it's a calendered fabric layered at a 45 degree angle, but that's just a guess since I'm not sure all that goes into the more high-tech fabrics.
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