As a proper noun trinity
is (christianity) in christian belief, the three persons (personae) of the godhead: father, son and holy spirit.
As a noun triplicity is
the quality or state of being triple or threefold; trebleness.
A group or set of three people or things; triad; trio; trine.
*:But when the moon rose and the breeze awakened, and the sedges stirred, and the cat's-paws raced across the moonlit ponds, and the far surf off Wonder Head intoned the hymn of the four winds, the trinity , earth and sky and water, became one thunderous symphony—a harmony of sound and colour silvered to a monochrome by the moon.
The state of being three; threeness.
* (group of three) threesome, triad, trio, trine, troika, triumvirate
* Trinity College
The quality or state of being triple or threefold; trebleness.
- In their trinal triplicities on high. — Spenser.