Green’s Dictionary of Slang

triangle n.

a three-way relationship, in any combination of sexes and sexualities.

[US]A.E. Duckett ‘Truckin ’round Brooklyn’ in N.Y. Age 4 Apr. 7/1: Ray Coleman is creating a triangle by paying loads of attention to Mae Johnson.
[US]W. Winchell On Broadway 19 May [synd. col.] At the Waldorf’s Starlight Roof: ‘She’s been in more triangles than a set of billiard balls.’.
[US]G. Legman ‘Lang. of Homosexuality’ Appendix VII in Henry Sex Variants.
[UK]‘Josephine Tey’ To Love and Be Wise 79: [S]he would think up some small exclusive thing to do with Walter; something [...] tête-à-tête. It had been too often a triangle lately.
[US]R.A. Wilson Playboy’s Book of Forbidden Words.

In compounds

triangular home (n.)

the Tyburn gallows, consisting of a three conjoined bars forming a triangle, capable of ‘turning off’ 21 victims at a time.

A. Smith Memoirs of... Jonathan Wild x: The Survivors, whom [...] he sends to their Triangular Home.

In phrases

on the triangle (phr.)

(UK und.) enduring a judicial beating [the triangular framework to which the victim was secured].

[UK]Thieves Slang ms list from District Police Training Centre, Ryton-on-Dunsmore, Warwicks 7: On the triangle: Being flogged.