Jay Street spans just one block — and this ultra-cool, six-level townhouse is the only single-family home on it.

In Lower Manhattan, you’ll find a precious handful of single-block streets, many of them paved in Belgian block. And to the downtown crowd, the most coveted of them all might be Jay Street, wedged between Greenwich and Hudson streets in the heart of the Tribeca West Historic District.

Dating to 1888, the building at 19 Jay Street was originally constructed by grocer John H. Mohlmann in the neo-Grec style, flaunting handsome cast-iron, brick, and stone details. Completely reimagined by Studio DB as a single-family townhouse, this exceptional residence now offers 9,000 square feet of interior space, with five bedrooms, five full bathrooms, and a ground-floor powder room. Showstopper add-ons include an indoor basketball court, a wine vault, a yoga studio, a climbing wall, a full-floor entertaining level, and a killer rooftop terrace with a grill, cocktail bar, mature plantings, and a vine-clad pergola.

One of the most remarkable things about this townhouse is the extraordinary amount of natural light that floods the expansive spaces, thanks to a central atrium with large skylights and glass flooring. Other winning architectural details include hardwood floors, exposed brick walls, 20-foot ceilings and double-height windows in spots, cast-iron beams and columns, cozy built-in niches for seating and lounging, designer lighting, and pocket doors. A smart-home Savant system controls the lighting, temperature, and security.

From the private street entrance, let’s take a floor-by-floor look at the 23-foot-wide home. First up is a grand entry gallery that leads to the ground-floor mudroom, a kitchenette, and a commanding teak-and-blackened steel staircase. Frosted glass doors open to the home’s two levels of recreation space — an astounding half-court basketball court set beneath nearly 13-foot ceilings, the climbing wall and a night-time entertainment area with a 100-inch drop-down screen.

Hop on the elevator or climb the stairs up to the second floor, which holds a guest suite with a private entry, a library nook, and a large flex space that could be a home office, a media room, or another bedroom. Up we go to the swank entertaining level, with an open-plan kitchen and living and dining rooms. The eat-in kitchen features a wide island with seating, marble countertops, custom oxidized maple and lacquered cabinetry, a walk-in pantry, and top-shelf stainless appliances. The double-height living room offers a Cararra marble fireplace and a striking wall of steel-and-glass doors that open to a Juliet balcony.

On the fourth floor, a mezzanine lounge overlooks the living room, and there’s also a bedroom with an adjoining study/homework space. The top-floor primary suite offers a fireplace, a wood-paneled dressing room, and an ensuite with a soaking tub, a shower, and dual vanities. Two more bedrooms linked by clever pocket doors round out the fifth floor.

Finally, it’s up to the dreamy rooftop deck and terrace. This swoon-worthy outdoor space boasts an indoor bar tucked into the bulkhead, plenty of privacy plantings, spaces for grilling and lounging, and big downtown views. Back down on the cellar level, you’ll find a 700-square-foot professional-level yoga studio and gym, a full bath, lots of storage, and the wine vault.

Wander around the neighborhood to find neighborhood staples like the Odeon, Frenchette, Sarabeth’s, and Locanda Verde. Lots of easy-to-get-to green spaces down here, too — Battery Park City, Hudson River Park, and Washington Market Park. For shopping, check out the nearby Whole Foods Market on Greenwich Street, the year-round Tribeca greenmarket, Brookfield Place, and Westfield World Trade Center. Can we all agree that this is still one of the coolest neighborhoods in the city?