International architects OMA have completed their latest addition to fashion house Prada’s arts complex in southern Milan, on the site of a former gin distillery.

Torre is a nine-level, 60m (197ft) high tower with a facade that alternates between glass and white concrete surfaces.

Devoted to “the development of a new typology for the exhibition of art” at Fondazione Prada, the structure’s different levels each have different spatial parameters, due to variations in plan dimensions, height and orientation. As a result, the height of the ceiling cumulatively increases with each floor.

Six of the nine levels are exhibition spaces, while the remaining three floors host a restaurant and other visitor facilities. A 160sq m (1,700sq ft) panoramic terrace tops the building.

The project was led by Rem Koolhaas, Chris van Duijn and project architect Federico Pompignoli.

Koolhaas said: “To extend the typologies offered by the Fondazione, a series of systematic variations is applied: each next floor is taller than the previous one, rectangular plans alternate with wedge shapes, the orientation of the rooms alternates between panoramic city views to the North, or narrower views in opposite directions, East and West.”

Torre joins OMA’s previous buildings, completed in 2015, for the 19,000sq m (204,500sq ft) arts complex – Podium, an exhibition pavilion at the centre of the compound consisting of a translucent gallery space on the ground floor and a second gallery space clad in aluminium foam; and Cinema, a multimedia auditorium with large bi-fold doors. The studio also clad a preserved building from the early 1900s, known as the Haunted House, in gold leaf, to create the attractions most famous landmark.

Seven existing buildings, that once served as warehouses, laboratories and brewing silos in the distillery, were also redeveloped as visitor and exhibition spaces.

Among OMA’s many previous completed cultural projects are the Design Museum in London and the recently-opened arts space Concrete in Dubai. They are currently creating the Factory cultural venue in Manchester and a striking theatre in Taipei, while expanding New York's New Museum and renovating the largest museum building in Russia.