Final answer:
Velvet is the fabric that has a third dimension and a deep surface texture due to the inclusion of an extra set of warp or weft threads. Other fabrics like chiffon, satin, and taffeta do not have this characteristic raised texture.
Step-by-step explanation:
The fabric with a third dimension due to an extra warp or weft set that is woven or knotted into the fabric, creating a deep surface texture, is velvet. Velvet fabrics are known for their soft and luxurious feel which is achieved through the technique of adding an additional set of warp or weft threads. These extra threads are incorporated to build up the nap of the velvet, which is the raised surface texture that gives velvet its distinctive look and feel.
Chiffon, satin, and taffeta are fabrics that do not have this third dimension in their standard forms. Chiffon is rather sheer and lightweight, satin has a glossy surface and a dull back, and taffeta is known for its crispness and smooth surface but does not have a raised texture like velvet.