δήμιος · dēmios — LSJ
belonging to the people, elected by the people, public, at the public cost, the sovereign people
belonging to the people, οἶκος Od. 20.264; αἰσυμνῆται δ. judges elected by the people, 8.259; πρῆξις δʼ ἥδʼ ἰδίη, οὐ δήμιος not public, 3.82; δήμιον ἦ ἴδιον; 4.314, cf. 2.32: epith. of Hestia at Paros, IG 12(5).238 (v B. C.): neut. pl. as Adv., δήμια πίνειν at the public cost, 11.17.250; τὸ δ. the sovereign people, A. Supp. 370, 699 (lyr.).
II public executioner
ὁ δ. (sc. δοῦλος) public executioner, Ar. Ec. 81, Pl. R. 439e, Lys. 13.56, Aeschin. 2.126, etc. (δάμιος μαστίκτωρ in A. Eu. 160 (lyr.)); ὁ κοινὸς δ. Pl. Lg. 872b.
2 public physician
public physician, πτωχὸς ἦν καὶ δ. Phoenicid. 4.13.
III
δημίαι πύλαι, perh. a mistake for Διομῇσι, Hsch.