A tower of jagged and jutting glass-faced apartments, “stacked” nearly 800 feet high, will rise like a giant game of Jenga over Tribeca.

The Alexico Group, developers of the $650 million project at 56 Leonard Street, at the corner of Church Street, released renderings of the long-anticipated designs. It is the first residential tower by the celebrated architecture firm of Herzog & de Meuron, whose work includes the redesign of London’s Tate Modern museum and the Beijing National Stadium in China.

The Switzerland-based architecture firm breaks down the old image of the high-rise as a sleek, hermetically sealed urban object to propose instead a thoughtful and daring new alternative – the iconic American skyscraper re-envisioned as a pixelated vertical layering of individually sculpted, graceful private residences opening to the atmosphere.

56 Leonard Street will be a 57-story residential condominium building in the Tribeca Historic District of downtown Manhattan, where it will rise above cobbled streets and historic 19th century neighbors. The tower will house 145 residences, each with its own unique floor plan and private outdoor space, in a veritable cascade of individual homes that the architects describe as “houses stacked in the sky,” blending indoors and outdoors seamlessly together.

The building’s 145 condominiums, due for completion in fall, 2010, will be priced from $3.5 million to $33 million.

Developer Izak Senbahar claimed he is confident that they will sell, despite Wall Street woes and the downturn in the economy. “It’s a big world,” he said, “and there’s a lot of money in the world, still.”