The Lift Sends Everyone to the Roof. Go There Second.

You will be funnelled towards the lift within about ninety seconds of entering, and the courtyard you crossed to get there is one of the strangest structures in the building. If you came in from Passeig de Gràcia, look up: the floor above you is carried by two concentric cylindrical girders tensioned by radial beams, the way a bicycle wheel works, spanning twelve metres on an eighty-centimetre structure. The mural tapestries on the walls are by the Symbolist painter Aleix Clapés. On the Passeig de Gràcia side they tell the love of Vertumnus and Pomona from Ovid; on the Provença side, the deadly sins alongside the heroes of the Trojan War.

The lift stops here. Resist the sign pointing outside and walk the attic first, while your slot empties onto the roof. Gaudí covered this floor with 270 brick catenary arches so the roof would not add weight to the building, and they stand on their own with no buttresses. Before it was the Espai Gaudí it was the communal laundry, the storage, the lift machinery and the building's thermal chamber: windows open in summer for the draught, shut in winter to trap the heat. The exhibition inside it is the only one in Barcelona that covers Gaudí's whole career rather than a single building, which is why it is worth doing before Park Güell and Sagrada Família rather than after. Walk the perimeter walkway too, and count the four cupolas shaped like Prussian helmets.

Six stairwell exits, the badalots, at seven metres each, with a spiral staircase inside every one. Twenty-nine chimneys at four metres, flues from a coal-fired central heating system that no longer exists, standing alone or grouped in twos, fives and sevens. Two ventilation towers at five metres that used to change the air in the attic you just left. The stone railing around the edge undulates in the same rhythm as the façade below it. Give this half an hour rather than fifteen minutes, and walk the full perimeter: the roof reads differently from each of its four sides.

A 1911 flat furnished as a Barcelona family would have had it, and the part of the visit people move through fastest. Look up. Gaudí drew the ceilings curved and had the plasterer reproduce circumferences, ellipses, spirals and scrolls over a braided reed frame, which is where the Spanish name techos planos de caña comes from. Some of them carry inscriptions. Then look at the doors: the sliding partition between living and dining rooms folds entirely into the side walls, and the front doors have iron-strip viewers so you could speak to someone without opening them. One absence explains the building: there is no main staircase. Gaudí got rid of it and gave the tenants lifts, which in 1911 was the radical part.