What's the best-kept secret on the historic-landmark circuit? More elegant than Mount Vernon, older than Ford's Theater and rumored to be haunted? The Octagon, owned by the American Institute of Architects Foundation, at 18th and New York Avenue NW; it also contains a more fanciful exhibit than many modern art galleries around town. The current show, "Architectural Fantasies: Creative Alternatives," has been extended through February 1.

Completed in 1800, the Octagon was a townhouse for Col. John Taylor, wealthy third-generation Virginia landowner and horsebreeder. It seems President Washington was pushing the sale of lots in the new Federal City and the Taylor family ended up with an irregular one, two blocks west of the White House. William Thornton, first architect of the U.S. Capitol, cleverly solved the problem by building an eight-sided mansion with round rooms and rectangular and triangular offshoots, used as closets. Throughout the house, windows, walls and doors are curved, a product of shipbuilding design.

Ring the bell at the bent front door and a hostess will show you around the fine quarters. A 1790 tabletop piano, Federal period furniture, the original Italian marble floor and ceiling molding -- minus 27 layers of paint stripped from the walls -- fill the three floors and basement.

The design and furnishings are characterized by simplicity and balance. A wide, oval staircase is the centerpiece; it's also the focus of well-worn rumors about a live-in ghost. One of the Taylor daughters, the story goes, had a fight with her father over her choice of boyfriend, fell over the railing or, variously, was thrown down the stairs, and was killed. There's no documentation for the episode, but some visitors swear they hear the daughter crying on the steps. Others say the ghost of a young girl in a gray dress appears on Halloween. Suit yourself.

In the drawing room, note the original terracotta mantle and portraits of the Thorntons by Gilbert Stuart; the dining room boasts a platewarmer in front of the fireplace, service for 12 and a cheese tray on casters; upstairs in the round Treaty Room, the only room that's roped off, President Madison signed the Treaty of Ghent, ending the war of 1812 with Britain (after being burned out of his quarters at the White House); the wine cellar and what would today be advertised as a "fully equipped eat-in kitchen" are reachable by a hidden servant's stairwell.

Upstairs, the fantastical show of visionary architectural pieces by Claes Oldenburg, David Macaulay, Philip Johnson and others includes a fun model and drawing for "Washington Monument Condominiums" by David A. Stainback -- a far cry from the days when a family could buy a lot with a walled garden in the commander-in-chief's neighborhood.