The Board of Appeals yesterday approved plans by Hexagon Properties to convert an 11-story office building on Commonwealth Avenue at Berkeley Street into nine condos.

Hexagon originally spent $30 million on the the building, constructed in 1895, to turn it into a social club aimed at millennials with disposable income, but withdrew those plans in the face of outrage from Back Bay residents. The company has instead purchased the Algonquin Club further down Comm Ave. for that purpose.

Hexagon attorney Mike Ross told the board the condos will range in size from 3,000 to 6,000 square feet. The largest unit, at the top of the building, will have exclusive access to a rooftop terrace by both stairs and a private elevator.

The company plans to install an unusual mechanical parking system in the basement for nine cars that would outdo even Mitt Romney's California parking elevator: The basement will actually have ten spaces; occupants will drive their cars into a "cabin," exit the car, punch in their access code and the cabin will go down to the basement and the car will be slid into an open space.

The Neighborhood Association of the Back Bay formally did not oppose the project. NABB's Susan Prindle, however, said members were "very pleased" that Hexagon listened to neighbors and dropped the social-club plans. She predicted the new residences will prove an asset to the neighborhood.

The mayor's office and City Councilor Josh Zakim also supported the proposal. Nobody spoke against it.