A short uphill walk east of the theatre brings you to the Martyrium of Saint Philip, an octagonal pilgrim church built around 400 AD on the spot where the apostle Philip is said to have been crucified upside-down in around 80 AD. The plan is unusual — a square outer wall enclosing an octagon, with eight chapels arranged like petals around a central worship space — and Italian archaeologists identified the building only in 2011, when they located the saint's actual tomb just downhill.
There are no roof or capitals left, but the layout is clear and the views back over the Pamukkale plain are wide. Bring sturdy shoes; the path up from the centre of the city is rough.