http://agathe.gr/democracy/the_prytaneis.html
The Prytaneis (Executive Committee) The senators administered their meetings themselves. Each tribal contingent in the Boule served in rotation for a period of 35 or 36 days as the Prytaneis, or Executive ... The building was famous for its roof shaped like a sun hat, which gave it the nickname skias, sunshade. The roof was made of diamond-shaped tiles, but their original arrangement is not known.