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“Twilled weave” is a weave type in which the warp wires and shute wires pass over two and under two in both directions. This is different from a plain weave, which is when the wires are woven one over and one under. “twilled weave” is often more pliable than a comparable plain weave wire mesh specification.in general, twilled weave is often used in filtration applications. The images below illustrate twilled weave, but because twilled weave is usually reserved for fine mesh, identifying a twilled weave usually requires a mesh counter.