Duomo Di Milano.

Climb the 250 steps (or take the lift) and you surface 65m up inside a forest of Candoglia marble — pink-veined, warm under the sun, prickling with 135 spires and gargoyles you couldn't see from below. Walk the buttress walkways slowly. Up here the medieval carvers got bored and got funny: among the saints you'll find boxers, grotesque faces, and on later restorations a rifle-toting WWI soldier and what locals swear is a tennis player.

At the top of the Guglia Maggiore stands the Madonnina — 4.16m of gilt copper, 33 hammered sheets, re-leafed with 6,750 squares of gold in 2012. She was hoisted up there in late 1774, and from August 1939 to May 1945 the city draped her in grey-green cloth so RAF bombers couldn't use her as a sighting point. Cardinal Schuster pulled the cover off on May 6, 1945.

Go to the northeast corner on a clear winter morning. The Alps line up behind her gold head like a stage backdrop — the single best photograph in Milan, and the reason Milanese still say sòta a la Madunina when they mean home.

Push through the bronze doors and the temperature drops ten degrees. Fifty-two pillars rise into the gloom — one for each week of the year, tradition says — holding up vaults so high your footsteps slap and double back as echo. The stained glass on the apse, some of the largest panels in the world, filters daylight into bruised reds and ultramarines that move across the marble floor as the hours pass.

Walk down the south transept until you hit Marco d'Agrate's San Bartolomeo Scorticato, carved 1562. The saint stands flayed, his own skin slung over his shoulders like a wet coat, every tendon and vein rendered with anatomist's precision. The Latin on the base reads Non me Praxiteles sed Marco finxit Agrate — "Not Praxiteles but Marc'Agrate made me." A 16th-century sculptor calling out a Greek master. The marble is cold to the touch and you will not forget it.

Before you leave, look up into the apse vault. A small red light glows between the ribs. It marks the Sacro Chiodo — a nail said to come from the Crucifixion, lowered once a year, every September 14, in a wooden cloud-shaped lift called the Nivola.

Just inside the main entrance, a brass strip runs across the marble pavement, inlaid with bronze zodiac signs. Most people step right over it. The Brera astronomers laid it down in 1786, and it still works: a pinhole 24m up in the southern nave vault drops a disc of sunlight onto the floor at solar noon, sliding along the strip as the year turns.

Go on a sunny day around midday, find your zodiac sign in the marble, and watch the sun mark the date. In winter the disc travels far down the nave toward Capricorn; in July it pulls in tight to the pillar base at Cancer. Same physics that ran the city's clocks before railways forced standard time. Then walk the few minutes west to the Monument to Leonardo da Vinci on Piazza della Scala — Leonardo lost the 1488 competition to design the Duomo's central spire, and the city eventually put him on a plinth round the corner anyway.