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The Temple of Orithena was founded in −2850 by Adrakhones, the father of geometry on Arbre. As an institution of learning, it is analogous to a Pythagorean school. Destroyed by volcanic erupation in −2621, its destruction lead to the beginning of the Peregrin period. Many of the survivors gravitate toward the city-state of Ethras.
During the period in which Anathem is set, the Temple is a partially excavated ruin on the island of Ecba run by a mathic-like institution with ties to the Lineage. Based on the timing of the institution's inception, just after the Third Sack, the organization may have been an evolution of the Knights of Halikaarn.
Prominent features of the temple include an Analemma on the temple floor, which is open to the sky, as well as a regular decagon on which the problem of the Teglon can be explored with tiles made from the original molds.