The headword is the present participle, masculine nominative singular, of the verb peripole/w; see generally LSJ s.v. (The quotation illustrates something connected but different: genitive singular of the adjectival use of peri/polos; cf. pi 1259, pi 1260, pi 1261.)
[1] The gloss is the present active participle, masculine nominative singular, of the verb peritre/xw, I run all around; see generally LSJ s.v. Identical glossing in the Synagoge, Lexica Segueriana 340.1, and Photius' Lexicon (pi745 Theodoridis), where the editor supports the view that the headword is quoted from Euripides, Iphigeneia in Tauris 1455.
[2] A stauro/s is only an upright stake, but in a ceremonial context as here, it connotes a cross, a structure intended for crucifixion; see LSJ s.v., II.
[3] Theophylact Simocatta, Histories 5.16.11-12; Whitby and Whitby, p. 76. The passage describes the entry of the Byzantine Emperor Maurice (539-602, emperor 582-602; mu 294) into the town of Rhamphos in the autumn of 590. This town's location is uncertain, but Theophylact's sequence of events places it along the Via Egnatia (Whitby, pp. 60-1), on the north coast of the Propontis (Sea of Marmara; pi 2578), between Rhegion (Barrington Atlas map 52 grid D3) and Selymbria (Selybria, Eudoxiopolis: Barrington Atlas map 52 grid C2; cf. sigma 307).