triarchy

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. Government by three people; a triumvirate.
2. n. A country governed by three rulers.

Century Dictionary and Cyclopedia

1. n. Rule by three persons; a three-headed government.

Wiktionary

1. n. Government by three persons; a triumvirate.
2. n. A country under three rulers.

GNU Webster's 1913

1. n. Government by three persons; a triumvirate; also, a country under three rulers.