This is a Mamluk kerchief embroidered with blackwork. It is linen with blue silk, 25 x 24.5 cm. The linen count is 22 threads per centimetre. It is currently in the Ashmolean.
I have charted the kerchief. I think the pattern would be reversible, as most of the Mamluk designs are. Please let me know how it turns out for you.