“‘—And He Built a Crooked House—'” is a science fiction short story by Robert A. Heinlein first published in Astounding Science Fiction in February 1941. The story is about a mathematically inclined architect named Quintus Teal who has what he thinks is a brilliant idea to save on real estate costs by building a house shaped like the unfolded net of a tesseract.
Quintus Teal, “Graduate Architect”, while drinking with his friend Homer Bailey, bemoans the conservatism of American architecture. He wants architects to be inspired by topology and the Picard–Vessiot theory. The conversation turns to four-dimensional objects and he shows Bailey three-dimensional models made of toothpicks and clay, representing projections of a four-dimensional tesseract, the equivalent of a cube. Bailey is baffled, but when Teal constructs an “unfolded tesseract”, a three-dimensional object, Bailey suggests building a house to that pattern. Teal, ever hungry for a commission, plies Bailey with more liquor until the contract is signed, as the story has it, “halfway down the second bottle”.
The house is quickly constructed, in its peculiar “inverted double cross” shape (having eight cubical rooms, arranged as a stack of four cubes with a further four cubes surrounding the second cube up on the stack) [see link]. However, the night before Teal is to show Bailey and his wife around the house, an earthquake occurs. The three of them arrive the next morning to find what appears to be just a single cubical room. Believing the top seven rooms to have been stolen during the night, they go inside to look for clues.
What they find is quite unbelievable: Not only are the upper floors completely intact, but the stairs seem to form a closed loop, in that the stairs from the top room lead back into the bottom room and not to the roof. What is more, there appears to be no way to get back out, because all the doors and even the windows lead directly into other rooms. At one point, they look down a hallway and are shocked to see their own backs. Teal eventually realizes that the earthquake caused the house to fold into an actual tesseract.
Teal tries to play up the benefits of the situation, but in attempting to move from one room to another by way of a French window, he falls outside and lands in shrubbery. Ever the optimist, he notes as he re-enters the house that they do have a way of leaving the structure after all. It seems to have something to do with their state of mind while passing through a window.
Exploring further, they find that the windows of the original top room do not connect where they mathematically “should”. One gives a dizzying view from above a skyscraper, another an upside-down view of a seascape. A third window looks out on nothing, that is, a place of no-space, with no color, not even black. The fourth window looks out on an unearthly desert scene. Opening the window they find the air on the other side breathable. Just then another earthquake hits, and so they exit in a panic, through the open window. They find themselves in a desert with unearthly, twisted, treelike vegetation around them, with no sign of the house or the window they just jumped through. They are only slightly relieved when they discover, from a passing truck driver, that they are in Joshua Tree National Monument, and not stranded on another planet.
Returning to the house, they find it has vanished. “It must be that on that last shock it simply fell through into another section of space”, Teal remarks. “I can see now that I should have anchored it at the foundations.”
PS. Isn’t the name Quintus Teal strangely reminiscent of Quinlan Terry?