The lambent new tower of art galleries Rem Koolhaas and his Rotterdam-based firm, OMA, have designed for the Prada Foundation is a chameleon. From the east, the elevation presents a slim, unadorned, milk-white concrete block, nine stories high, punctured by loggias — a signpost, like the traditional village bell tower, rising above a low, scruffy neighborhood.

To the north, where the facade meets Milan’s skyline and becomes mostly glass, cantilevering over the street, the block breaks into a zigzag of shifting floor plates, rectangles and trapezoids, the whole building wedged onto a triangular plot. The south end makes plain how the structure stands up. An ensemble of enormous cables encased inside a giant beam counteracts the thrust of all those heavy, cantilevered concrete decks. Like a sword in a stone, the beam angles from the top of the tower through the red-tiled roof of an adjacent former warehouse, anchoring in the floor below.