Usage: 4 forms in 6 verses
Form Translated As     In Verse(s)
περιώδευσαν they traveled about LXX.2Sam.24.8LXX.Zech.6.7
περιωδεύκαμεν We have traveled about LXX.Zech.1.11
περιοδεύσατε travel about LXX.Zech.6.7
περιοδεύσαι to travel about LXX.Zech.1.10LXX.Zech.6.7

Liddell-Scott-Jones

περιοδεύω (periodeuō) to travel about G:V

περιοδεύω-εύω,

go all round, τὴν γῆν [LXX+3rd c.BC+]; τὸ Παλάτιον [LXX+1st c.AD+]; make a revolution, of the moon, [Refs 2nd c.AD+]

__2 in military sense, patrol, [Refs 4th c.BC+]; of dyke-watchers, [Refs 3rd c.BC+]; of an inspector, go round vineyards, [Refs 3rd c.BC+]; march round, [Refs 2nd c.AD+]
__II metaphorically, go systematically through, βίον τινός [Refs 1st c.AD+]; study diligently, [Refs 4th c.BC+]; περιοδεύωευομένη φαντασία Academiciap.[Refs 2nd c.AD+]
__III circumvent, cheat, [Refs 1st c.AD+]
__IV practise, of a midwife, [Refs 2nd c.AD+]; οἱ περιοδεύωεύοντες practitioners, [Refs 6th c.AD+]:—passive, to be treated, [Refs]
__V Rhet., write in periods, [Refs 4th c.BC+]; διαπορητικῶς π. [Refs 2nd c.AD+]:—passive, περιωδευμένη προφορὰ καὶ γραφή [Refs 5th c.BC+]; but τὸ περιωδευμένον path traversed in a circle, explanation of περίοδος, [Refs 4th c.BC+]

LSJ Scripture Refs: LXX.Zech.1.10LXX.2Kgs.24.8