The popular nickname of the region is a misnomer as, astrographically, it's only a triangle in cross section, looking "down" from "above" the plane of the galaxy. Its true shape in three dimensions is more that of an hourglass with a roughly triangular cross-section.
In 2275, Gibraltar -- an unwanted world situated between the Federation and the Romulan Star Empire -- becomes one of the most important in the Triangle when the two governments choose it as the site for negotiating a settlement. Also, during that year, Klingons occupy the Triangle world of Marram IX. (FASA RPG)
Shadowstar Station's construction was authorized by the Federation Council's Military Staff Committee in 2286. The station's primary raison d’être was to serve as primary customs house for commercial traffic in and out of Triangle space. (Star Trek: Shadowstar Station)
Following the Khitomer Accords of 2293, the Federation expanded its territories into the Triangle as the New Colonies. Starbase 52 was constructed as the liaison facility between the New Colonies and the Federation heartworlds. (Star Trek: Accord)