BARI, Italy — At Castel del Monte, the stage is set for tragedy or black magic. Clouds scuttle across the sky, and a full moon rises. Footsteps echo on cold stone, startling pigeons into flight.

A medieval emperor hunted with falcons and cheetahs here, consulted astrologers and slept on Oriental silk.

Local people sought refuge during the plague, and brigands hid out in the castle. Vandals over the years stripped it, leaving little more than an empty shell on a lonely hilltop at the edge of the Murge, a barren-looking limestone plateau worlds apart from the sunny Italian south most people know.

This medieval masterpiece, begun in 1240 — about the same time as Westminster Abbey — has eight sides, linked by eight eight-sided towers.

Its seemingly endless repetition of the octagonal form has haunted mathematicians through the ages, who see it as a work of pure geometry. The more mystically inclined impute occult significance to this temple of the octagon, noting that great buildings around the world, such as Jerusalem's 1,300-year-old Dome of the Rock, also have eight sides.

Whether icon or equation, the castle has more vibes than "The Da Vinci Code," as I discovered. I love a good mystery. And Castel del Monte is surely one, a model for the labyrinthine library in Umberto Eco's 1983 medieval whodunit "The Name of the Rose." I stood in the castle's deserted courtyard at dusk, nerves taut, heart thumping, ears pitched, wishing the walls could talk.

But Castel del Monte, as silent as a sarcophagus and as strange as a UFO, keeps its secrets, glowing like the crown of its 13th-century builder, Holy Roman Emperor Frederick II.

Cultured and brutal, despotic and enlightened, a Christian crusader who was excommunicated, Frederick left a legacy still debated by historians, including David Abulafia, author of the recent biography "Frederick II: A Medieval Emperor." In his time and after, Frederick was called stupor mundi (the wonder of the world) and the Antichrist.

A 1927 biography of Frederick by German historian Ernst Kantorowicz was a favorite of Adolf Hitler, whose delusions of grandeur were fueled partly by the emperor's efforts to consolidate a realm that included Germany, the Netherlands, Austria, Poland, parts of France and Italy, Malta, Cyprus, Israel and Lebanon.

To oversee his vast domain, Frederick traveled widely and incessantly, taking with him his crown jewels and library, elephants, camels, hunting birds, bodyguards, poets who created the sonnet and mathematicians who gave Western civilization Arabic numerals.

Of all the lands he ruled, he loved low-lying Puglia best, in those days a richly forested region bordered on the east by the Adriatic Sea. Here he built his startling octagonal castle, part hunting lodge, part pleasure palace, part symbol of his might.

Among great architectural ciphers, Castel del Monte stands out for its stubborn unlockability, although it is less well known than others chiefly because it is in the relatively untrammeled, disreputable Mezzogiorno, at the heel of the Italian boot.

Warnings about the region's poverty and crime rang in my ears. I wore a money belt and resolved not to let my guard down, especially in Bari, the Puglian capital of 300,000, where I began my explorations.

I had planned to pick up a rental car and drive into the city, but I got cold feet on the plane from Rome, remembering an acquaintance who narrowly avoided a carjacking when she went astray in Bari. So I took a cab from the airport through the city's unlovely industrial outskirts and was safely deposited at the Palace Hotel, a modern high-rise close to the city's center.

My room's decor was so dated that it looked as if Pat Nixon had conceived the design. But it lacked no amenities.

Every meal I ate in Puglia was memorable, starring fish from the Adriatic and produce from the plains northwest of Bari known as the Tavoliere, which means chessboard. Its farms, geometrically laid out by the ancient Romans, yield what many consider Italy's best olive oil, as well as almonds, fruit, cheese and grapes for the region's red wines.

But in Puglia's capital you're surrounded by a workaday port (largely devoted to petroleum shipping), gritty suburbs and a maze of deteriorating streets.

Even 800 years later, Frederick II still casts a long shadow across southern Italy. Streets, piazzas, trattorias and even laundries in Bari are named for him. One of the many fortresses he built or renovated stands on the waterfront, moated and walled. Sculptural details on its western portal, as finely wrought as an illuminated manuscript, include Frederick's symbol, an eagle clutching a lion in its claws.

I picked up a rental car after touring Bari and had no trouble finding my way up the coast, first to Trani, a quiet town with another Frederican castle dating from 1233 and an exquisite Puglian Romanesque cathedral.

San Nicola Pellegrino, the third of three churches built one on top of the other, has a tall, elegant campanile and a fancifully decorated facade featuring the animals in Frederick's menagerie, including elephants.

Barletta, about 10 miles north of Trani, has another striking Puglian Romanesque cathedral and was where Frederick launched a crusade in 1228 to liberate then-Muslim-controlled Jerusalem, after repeated promptings from Pope Gregory IX. The emperor's tardiness in getting started got him drummed out of the church.

At a time when theologians were criticizing Rome's worldliness and hedonism, Frederick came to be seen alternately as God's chastising instrument and the Antichrist.

After my one night in Bari, I took a room in a fortified farm, or masseria, within sight of Castel del Monte, about 40 miles northwest of Bari. Like many other masserias in rural Puglia, the rambling farm complex welcomes tourists. Accommodations are in a recently built wing of simple but comfortable guest rooms, where the sheets and towels bear the crest of owner Salvatore Tannoja, whose family was ennobled around 1770.

It stayed cold and foggy while I was here, which made Frederick's castle seem all the more haunting, especially at night when its ramparts are illuminated. You can see Castel del Monte from miles away. A winding road leads past vineyards and orchards, then through a pine forest on its way up to the castle, which I first visited at dusk.

It's a stiff climb from the parking lot to the portal, a triumphal arch on the east side, sculpted of rose-colored breccia. Except for the main entry and a handful of small mullioned windows, the exterior walls are blank.

Inside the octagon, the rooms are arrayed around an eight-sided courtyard and open onto one another with no corridors. The towers between them have vestiges of 13th-century latrines, vaulted Gothic ceilings and spiral staircases leading to the second story, almost a mirror image of the first. Although most of the castle's embellishments are long gone, some marble fireplaces, graceful three-tiered columns and cunningly sculpted capitals remain.

Frederick stopped occasionally at Castel del Monte to indulge his passion for hunting.

Around 1248, the emperor wrote "The Art of Hunting with Falcon," a treatise that survives as an illustrated manuscript in the Vatican's library.

In it, Frederick identified himself as "one who cared nothing for the size of the kill but only for the thread of understanding between man and bird, the skill that enabled a man to extend his will into the sky and to draw back his emissary from the clouds."

That is the man I thought of rattling around his castle in the dying light, not the heretical monster abhorred by the pope or the medieval tyrant admired by Hitler, although historians suggest he may have been something of both.

Good and bad at once. Maybe that's the real riddle of Castel del Monte.