It has been suggested that the greek word φαιλόνην,as St Paul uses it in 2 Timothy 4:13 has a link to the shroud of Turin, as a early relic of Christianity; with links to the mendalion of the 4th century in Eddessa.
τὸν φαιλόνην ὃν ἀπέλιπον ἐν Τρῳάδι παρὰ Κάρπῳ ἐρχόμενος φέρε, καὶ τὰ βιβλία μάλιστα τὰς μεμβράνας. (2 Tim. 4:13, NA27)
Penulam, quam reliqui Troade apud Carpum, veniens affer tecum, et libros, maxime autem membranas. (Ed. electronica, 2 Tim. 4:13, Biblia Sacra juxta Vulgatam Clementinam)
When you come, bring the cloak I left with Carpus in Troas, the papyrus rolls, and especially the parchments. (2 Tim. 4:13, The New American Bible)
Is there any mileage in this suggestion.