A faille was a kind of hood or veil worn by women during the 16th and 17th centuries.
Faille is a light, soft, glossy silk or rayon cloth fabric with a cross-wise rib effect. It is similar to grossgrain, but much softer. It has been used since the mid 19th century in the manufacture of women's garments, especially coats and dresses. Research Faille
 
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