Just before dusk on a sharp bend in Florida Avenue NW, a very pregnant Alice Speck smashed a bottle of champagne across the prow of her new house. Husband Jeff Speck, who designed the startling triangular dwelling, stood close enough to revel in the fizz. After two years of dreaming, sleuthing and coaxing to acquire a tiny flatiron plot at 10th Street, and 15 months of exacting construction to build on it, the couple was finally able to call their brick-and-glass aerie home.

“The story of this house is breaking a whole lot of rules,” says Jeff, an urban planner and former design director of the National Endowment for the Arts.

The three-story house measures about 500 square feet per floor, but on this evening in June, sparkling glass-fronted balconies and banks of cantilevered windows glowed with larger promise. Herbs had rooted in a patio garden beside the sidewalk, and a Marimekko-clad antique rocker awaited the Specks’ first child, Milo, born days after the house was christened. A coterie of friends equally passionate about contemporary urban architecture traipsed up and down the house’s immense spiraling steel staircase and took turns outside, ogling the handmade bricks that bring this residence to its dramatic conclusion.

“A flatiron lot tells you what the house wants to be,” Jeff says.

Wedge-shaped flatirons are the archetypal lot in the nation’s capital, a quirk created when George Washington’s planner, Pierre Charles L’Enfant, sliced the street grid with diagonal boulevards, and Jeff was determined to have one. He found such a lot on a block of Florida Avenue bounded by 10th and W streets, which appears clearly on a 1792 master plan. Despite the renaissance along nearby U Street, two end lots at the narrow tip remained bereft of life, their tiny turn-of-the century rowhouses long ago replaced by dereliction and weeds.

It took a private detective to locate the owners, payment of back taxes to gain clear title and a fistful of variances from the D.C. Board of Zoning Adjustment before the Specks could build. Through lengthy negotiations over an unconventional design, and approval from the Public Space Committee of the D.C. Department of Transportation, Jeff was able to extend the upper floors beyond the confines of the house’s triangular footprint.

“I bought this lot knowing I was taking a huge risk,” he says.

Jeff picks up a cardboard model to explain how his ideas evolved into a puzzle of geometry -- “a wood rectangle dropped into a brick triangle.” The triangular footprint mirrors the converging sidewalks, but the upper floors -- the rectangle -- break free with cantilevers and balconies. As a result, the house appears to be a triangle from the street but is straightforward inside. In the living room, a course of exposed brick between glass and wallboard brackets the cantilever, establishing a visual reminder where the rectangle meets the triangle.

“Without the cantilever, it wouldn’t have worked,” Jeff says. With it, he believes he achieved “the biggest 12-by-12 living room you’ll ever be in.”

Alice, 30, and Jeff, 45, were apartment dwellers with a shared passion for art, history and city living when he decided to design “my first house.” A custom residence and office would become a three-dimensional calling card as Jeff set up as an independent planner. But the house was more than a vanity project.

“Alice is the client,” he says. “From the beginning, I knew I had to create a plan to satisfy what she needed in a house for a family.”

So, Jeff carved out a media room, a closet big enough for a stroller, and a laundry and full bath next to his office on the first floor. One flight up, the heart of the house unfolds asan open-plan kitchen, at Alice’s insistence, with a full viewof the staircase through an interior window. Black cabinets and concrete counters stained to match the inky stairs contrast with a bright, white living room. A small balcony and expanses of glass, some clear, some translucent, offer a view across Florida to the escarpment that formed the natural boundary of L’Enfant’s Washington.

“I love all the light coming in both sides from the windows,” Alice says. “We really feel like we’re in the trees.”

On the top floor, two bedrooms share a spacious bathroom. The master bedroom benefits from a balcony with a vista of the Washington Monument. A curtain can be pulled across the stair landing to define a dressing room.

A steel staircase, weighing nearly five tons, makes it all work. Jeff playfully drops a marble into the hollow stair rail. It pings its way to the basement, rolling to a stop at the guest room door. Steel reappears as the floor of triangular stair landings and as the structural support for a window seat.

Jeff credits Alice with making the critical suggestion to locate the staircase in the southeast corner of the triangle. That freed up precious square footage on each floor. “You can have an instinct, but on a tight lot, you don’t know until you draw it,” he says.

There are no pointed rooms. The angle that appears so prominent on the exterior is hidden in a closet on the first floor, occupied by a wood-burning fireplace on the second and houses the chimney on the top floor. “I knew I didn’t want to occupy the point,” Jeff says. “It’s better to look at than to be in.”

Jeff came more naturally to contemporary architecture than did Alice, who grew up with traditional houses and split-rail fences in the Midwest. His childhood was spent in a suburban Boston house designed by an apprentice of the modernist master Walter Gropius. After earning a master’s in architecture at Harvard on his way to becoming a certified city planner, he worked for the new urbanist planning and architecture firm of Duany Plater-Zyberk & Co. He calls himself “lead designer” on the house, which was finalized with help from an architect friend, Brie Husted.

The house was not simple to build. The cantilevers required a steel frame for support, and oversize panels of glass, including interior window walls in the kitchen and Jeff’s office, demanded special handling. A polished concrete slab intended for a console between dining and living areas was incorrectly measured but found a new purpose as a seating element outside the front door.

“Tolerances were very small,” Jeff allows, and “some things had to be built twice. Flatiron lots are not the solution if you want to save money.”

As a professional advocate of sustainable design, Speck insisted on going solar at home. The house has a 12-panel, 2-kilowatt system of photovoltaic cells on the roof. Other features include a solar water heater, dual-flush toilets, radiant heating under the sub-flooring and high-velocity air-conditioning, which avoided intrusive ductwork.

Today, neighbors include Howard University and the National Park Service, which owns a triangular patch of lawn just beyond the point of the house. One can imagine it as the site of some future national pocket park, but for now, the star on the block belongs to the Specks.

Jeff worked hard to make sure the new house would fit in. He maintained the 19th-century rhythm of punched windows of the adjacent rowhouses and nodded to the industrial loft aesthetic of a university building across 10th Street. But the distinctive angles and expanses of glass exude a bold 21st-century spirit.

For Alice, the biggest surprise has been the lack of noise around the urban site. “On weekends and nights, Florida Avenue is really quiet,” she says. “When we eat out on the balcony, we feel like we’re in this really dense area, but it’s all ours.”

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