trialogue
A conversation or talk between three people.
uncommon
Only for a short while was he kept waiting. The trialogue came to a close, followed by a brief interval of silence—at the end of which the canoe once more made its appearance upon the open water of the lagoon.
An informal tripartite meeting attended by representatives of the European Parliament, the Council of the European Union, and the European Commission.
Where it comes from
From tri- + -alogue, formed on the analogy of dialogue, where the first syllable is interpreted as di-. Compare Medieval Latin trialogus. Note that official documents of the European Union use the spelling trilogue (perhaps influenced by the French spelling).
Adapted from the Wiktionary entry trialogue (CC BY-SA 4.0).