The Thrice-Great are a Legacy that applies the Ptolemaic model of the universe to the struggle to reach the Supernal Realms and invented a doctrine called Hermeticism to aid their attempts to bridge the Abyss and follow the Exarchs and the Oracles by communicating with the spirits of planets.
The Thrice-Great began during the Hellenistic period between the conquests of Alexander and the Roman Empire. In this period, Greek philosopher-scientists tried to devise a rational model of the universe. The resulting system received its definitive statement by the astronomer Claudius Ptolemy. The Earth, he said, occupied the center of the universe. Around the Earth, concentric crystal spheres carried the Sun, Moon, planets, and finally the fixed stars. The founders of the Thrice-Great understood that the stars were merely a symbol for the Supernal World; they tried to Ascend by way of the Shadow Realm and the planetary spirits who dwelled there. They did not beg or pray, either. The Thrice-Great believed that a mage who found the right formulas could command, and the gods themselves would obey. They believed (or discovered) that each planet bore mystic affinities to phenomena on Earth: Plants, animals, parts of the human body, gemstones, metals, colors, musical tones, and numbers. By adding these substances and qualities to their spells, they could attract the forces and spirits of a particular planet - and compel them.
The Hermetics organize themselves in lodges that act as diffuse Consilia, with their own officers, bylaws, oaths, and rituals. Stargazers are supposed to bring their problems and disputes to their lodge leaders, not their Consilium - a bit of secrecy other mages do not appreciate. Stargazers obsess over ranks, titles, and other indicators of power and (supposedly) progress up the Planetary Ladder. Lodges tend to schism every time there's a conflict in leadership, or even fall apart completely. Some lodges also refuse to acknowledge other lodges as "genuine" Thrice-Great. Depending on whom you ask, the Legacy includes anywhere from six to 15 lodges. Hermetics sometimes abandon one lodge for another, so the lodges lack well-defined territories.