The Homomda are a major galactic race, somewhat further advanced than the Culture, but not yet as removed from the material universe as the Dra'Azon or the other Sublimed civilisations. They see themselves as acting as a balancing factor between other major races.
The Homomda have a tripedal, pyramid-formed structure. It is later mentioned in Look To Windward that they have glistening black skin, three arms, three ears, a large mouth and stand somewhat taller than a human.
Among the history revealed about the Homomda is that they gave shelter to the 'Holy Remnants' of the Idiran species when they were driven from their world and almost made extinct by another species. They used the Idirans (who share similarities to their tripedal form) as elite mercenary troops and later helped them reconquer their homeworld and expand their own sphere of influence. In the Idiran-Culture War, they supported the Idirans against the Culture, due to a policy of trying to prevent one species (or group) from attaining too much influence in the galaxy, similar to real-world Great Britain before World War I.
After sustaining heavy losses during the decades-long war - even with their ships being described as more powerful than most Culture ships (Appendices of Consider Phlebas) - they eventually struck a truce with the Culture and withdrew from the conflict. This was a major factor in the eventual Idiran defeat.
In Look To Windward it is noted that the Homomda consider the Culture to be immature, impulsive - childish, in a word. However, the Homomdan character central to the novel feels warmth for his Culture friends, and finds himself increasingly changing from an 'Ambassador' to a Culture citizen. Indeed, it is revealed later on that Culture citizens refer to him as 'Ambassador' not because they believe he represents the Homomda to the Culture, but rather the other way around.
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