basket

1. A stiff, woven container. "A tisket, a tasket, a green and yellow basket..."

2. The enclosure at the top of personnel lift.

3. Type of wrap used with a wire rope sling around a beam, or a polyester round sling around a truss chord.

http://www.ia470.com/primer/rigging.htm
See http://www.gripsure.com/Round_Slings.html for comparison of how different wraps affect strength. Compare/contrast basket with choke and straight lift (vertical).