Everybody hates K Street, by which most mean those blocks redeveloped with bland International Style knockoffs in the ‘70s and ‘80s. And yet that type of K Street building remains the model for office buildings throughout the city. Given D.C.’s height limitations and zoning rules, as well as developers’ desire to construct every leasable square foot they can, featureless rectangles continue to rise. The brief 1980s and ’90s vogue for historicist designs has had some effect—more masonry, less glass—and some new boxes are partially hidden by preserved historic buildings, or at least their facades. Still, there aren’t a lot of new ideas out there.

Now there’s one, and it’s become common enough in one neighborhood that the area could even named for it. North of Penn Quarter, here comes the emerging Wedgie District.

The wedgie is an angular bulge from an otherwise banal office block, generally a glass-covered protuberance from a brick- or stone-clad structure. With the addition of a new one at 10th and F Streets NW, there are now three of them in as many blocks.

The first wedgie juts from the building that covers most of the south side of H Street NW between 9th and 10th Streets. (It’s the Secret Service headquarters, although the General Services Administration likes to pretend no one knows that.) The building is mostly tan brick, and basically looks like an outsized ’60s high school. But near the east end, a glassed triangle pokes out, as if the larger building were giving birth to an all-glass K Streeter.

This building was followed by Pepco headquarters, dubbed Edison Place, on the northeast corner of 9th and G. Here the wedgie is on the corner, and has a bit of a curve to it. From the corner, the bowed protrusion actually looks as if it is the building. But move east or north, and it’s revealed as a wedgie.

The newest wedgie is at 10th and G, part of a new office building stuck crudely behind some older edifices, including the facade of the Atlantic Building (former home of the 9:30 Club). The main structure is remarkably similar to the Secret Service building—same shade of brick—but features several wedgies. One, tall but shallow, towers above the mansard-roofed house at the corner. Another one, bolder but only about a story higher than the house, flares further down 10th Street. These wedgies seem a rude attempt to upstage the existing structures; they clash with the streetscape without creating a rhythm of their own.

Ironically, the angle is a naturally occurring shape in L’Enfant’s street plan, and the triangles and trapezoids created by the intersections of streets and avenues have, occasionally, yielded interesting buildings, notably the National Gallery’s East Building. A triangular prow—used in a classical, symmetrical mode—also works well in the skinny ’80s office building at 816 Connecticut Ave. NW.

The wedgie, however, is neither a fundamental principle, as in the East Building, nor a central decorative motif, as at 816 Connecticut. It’s just an offhand gesture in a neighborhood that was remade too hastily, with too little thought, and with only the basic zoning rules as guidance. As on K Street, these buildings were built to maximize rentable space, with any design elements that would hinder that severely circumscribed. That’s why the wedgie comes on like a bold gesture but actually ends up looking weak.