You'll see Castel del Monte, an inhumanly exact geometric shape on a hilltop, from miles away. Mysterious and perfectly octagonal, it's one of southern Italy's most talked-about landmarks and a Unesco World Heritage Site. No one knows why Frederick II built it – there's no nearby town or strategic crossroads. It was not built to defend anything, as it has no moat or drawbridge, no arrow slits, and no trapdoors for pouring boiling oil on invaders.
Some theories claim that, according to mid-13th-century beliefs in geometric symbolism, the octagon represented the union of the circle and square, of God-perfection (the infinite) and human-perfection (the finite). The castle was therefore nothing less than a celebration of the relationship between humanity and God.
The castle has eight octagonal towers. Its interconnecting rooms have decorative marble columns and fireplaces, and the doorways and windows are framed in corallite stone. Many of the towers have washing rooms with what are thought to be Europe's first flushing loos – Frederick II, like the Arab world he admired, set great store by cleanliness.
To get to the castle without a car, take the Ferrovia Bari-Nord train from Bari to Andria, then bus number 6 from Andria station to the castle (35 minutes, five daily, April to October only). The castle is about 35km from Trani; there's no parking, but a nearby site charges €5 for a car, and €1 for a shuttle up the short, steepish 500m to the castle.