Apartments in Paris, like many cosmopolitan cities around the world, are very expensive. Monthly rent for a 900-square-foot space in an upper-middle-class neighborhood is, on average, about $2,250. That is one reason why, a few years ago, Paris mayor Anne Hidalgo released a statement saying, “A city like Paris must be able to reinvent itself at every moment in order to meet the many challenges facing it. Particularly in terms of housing and everything relating to density, desegregation, energy, and resilience.” This call to action led to Réinventer Paris, a competition for contemporary urban projects aimed to shape the future of the French capital.

Of the initial 858 applications from 15 different countries around the globe, it’s a design by Paris-based Marin + Trottin Architecture that has been creating the most buzz. The proposal, titled Paris par nous, Paris pour nous, is for a residential building in the 13th arrondissement that would offer multiple types of housing to meet the needs of a diverse group of residents. From smaller studio units for younger or less affluent patrons, to two-bedroom or larger abodes for growing families, to mansion-style apartments for wealthy buyers, the design was created, in part, to represent the various ways that Parisians are living today. The result comes together almost as if it were a game of architectural tetris, with units of different shapes and sizes built next to, and on top of, one another.

The building would offer more than 100 units to buy or rent.

In the coming days, the winners of the Réinventer Paris competition will be announced. Their proposals, along with those of all 74 finalists, will be presented February 4 at an exhibition in the Pavillon de l’Arsenal. From more information visit pavillon-arsenalom/fr/expositions .