A group of three novels or plays, each complete in itself

One word substitute is Trilogy.

Triplet: one of three children or animals born at the same birth.
Triumvir: (in ancient Rome) each of three public officers jointly responsible for overseeing any of the administrative departments.
Trilogy: a group of three related novels, plays, films, etc.
Trivet: an iron tripod placed over a fire for a cooking pot or kettle to stand on.