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The fabric I use for these large tallitot is silk noil, also called raw silk. It's not at all slippery, comes in many colors, and looks great with accents of dupioni silk.
This large tallit (42x72 inches) is made of a light grey silk noil, with stripes of two different blues pieced in so that the color shows on both sides. The atarah repeats the two blues, and the white embroidery creates a balance with the tzitzit.