"What’s that supposed to be?" Bailey demanded suspiciously.

"That’s a tesseract, eight cubes forming the sides of a hypercube in four dimensions."

"It looks more like a cat’s cradle to me. You’ve only got two cubes there anyhow. Where are the other six?"

"Use your imagination, man. Consider the top of the first cube in relation to the top of the second; that’s cube number three. Then the two bottom squares, then the front faces of each cube, the back faces, the right hand, the left hand—eight cubes." He pointed them out.

"Yeah, I see ’em. But they still aren’t cubes; they’re whatchamucallems—prisms. They are notquare, they slant."

"That’s just the way you look at it, in perspective. If you drew a picture of a cube on a piece of paper, the side squares would be slaunchwise, wouldn’t they? That’s perspective. When you look at a four-dimensional figure in three dimensions, naturally it looks crooked. But those are all cubes just the same."

"Maybe they are to you, brother, but they still look crooked to me."

Teal ignored the objections and went on. "Now consider this as the framework of an eight-room house; there’s one room on the ground floor—that’s for service, utilities, and garage. There are six rooms opening off it on the next floor, living room, dining room, bath, bedrooms, and so forth. And up at the top, completely enclosed and with windows on four sides, is your study. There! How do you like it?"

"Seems to me you have the bathtub hanging out of the living room ceiling. Those rooms are interlaced like an octopus."

"Only in perspective, only in perspective. Here, I’ll do it another way so you can see it." This time Teal made a cube of toothpicks, then made a second of halves of toothpicks, and set it exactly in the center of the first by attaching the corners of the small cube to the large cube by short lengths of toothpick. "Now—the big cube is your ground floor, the little cube inside is your study on the top floor. The six cubes joining them are the living rooms. See?"

Bailey studied the figure, then shook his head. "I still don’t see but two cubes, a big one and a little one. Those other six things, they look like pyramids this time instead of prisms, but they still aren’t cubes."

"Certainly, certainly, you are seeing them in different perspective. Can’t you see that?"

"Well, maybe. But that room on the inside, there. It’s completely surrounded by the thingamujigs. I thought you said it had windows on four sides."

"It has—it just looks like it was surrounded. That’s the grand feature about a tesseract house, complete outside exposure for every room, yet every wall serves two rooms and an eight-room house requires only a one-room foundation. It’s revolutionary."

"That’s putting it mildly. You’re crazy, bud; you can’t build a house like that. That inside room is on the inside, and there she stays."

Teal looked at his friend in controlled exasperation. "It’s guys like you that keep architecture in its infancy. How many square sides has a cube?"

"Six."

"How many of them are inside?"

"Why, none of ’em. They’re all on the outside."

"All right. Now listen—a tesseract has eight cubical sides, all on the outside. Now watch me. I’m going to open up this tesseract like you can open up a cubical pasteboard box, until it’s flat. That way you’ll be able to see all eight of the cubes." Working very rapidly he constructed four cubes, piling one on top of the other in an unsteady tower. He then built out four more cubes from the four exposed faces of the second cube in the pile. The structure swayed a little under the loose coupling of the clay pellets, but it stood, eight cubes in an inverted cross, a double cross, as the four additional cubes stuck out in four directions. "Do you see it now? It rests on the ground floor room, the next six cubes are the living rooms, and there is your study, up at the top."

Bailey regarded it with more approval than he had the other figures. "At least I can understand it. You say that is a tesseract, too?"

"That is a tesseract unfolded in three dimensions. To put it back together you tuck the top cube onto the bottom cube, fold those side cubes in till they meet the top cube and there you are. You doll this folding through a fourth dimension of course; you don’t distort any of the cubes, or fold them into each other."

Bailey studied the wobbly framework further. "Look here," he said at last, "why don’t you forget about folding this thing up through a fourth dimension—you can’t anyway—and build a house like this?"

"What do you mean, I can’t? It’s a simple mathematical problem—"

"Take it easy, son. It may be simple in mathematics, but you could never get your plans approved for construction. There isn’t any fourth dimension; forget it. But this kind of a house—it might have some advantages."

Checked, Teal studied the model. "Hm-m-m— Maybe you got something. We could have the same number of rooms, and we’d save the same amount of ground space. Yes, and we would set that middle cross-shaped floor northeast, southwest, and so forth, so that every room would get sunlight all day long. That central axis lends itself nicely to central heating. We’ll put the dining room on the northeast and the kitchen on the southeast, with big view windows in every room. O.K., Homer, I’ll do it! Where do you want it built?"

"Wait a minute! Wait a minute! I didn’t say you were going to build it for me—"

"Of course I am. Who else? Your wife wants a new house; this is it."

"But Mrs. Bailey wants a Georgian house—"

"Just an idea she has. Women don’t know what they want—"

"Mrs. Bailey does."

"Just some idea an out-of-date architect has put in her head. She drives a new car, doesn’t she? She wears the very latest styles—why should she live in an eighteenth century house? This house will be even later than this year’s model; it’s years in the future. She’ll be the talk of the town."

"Well—I’ll have to talk to her."

"Nothing of the sort. We’ll surprise her with it. Have another drink."

"Anyhow, we can’t do anything about it now. Mrs. Bailey and I are driving up to Bakersfield tomorrow. The company’s bringing in a couple of wells tomorrow."

"Nonsense. That’s just the opportunity we want. It will be a surprise for her when you get back. You can just write me a check right now, and your worries are over."

"I oughtn’t to do anything like this without consulting her. She won’t like it."

"Say, who wears the pants in your family anyhow?"

The check was signed about halfway down the second bottle.

Things are done fast in southern California. Ordinary houses there are usually built in a month’s time. Under Teal’s impassioned heckling the tesseract house climbed dizzily skyward in days rather than weeks, and its cross-shaped second story came jutting out at the four corners of the world. He had some trouble at first with the inspectors over those four projecting rooms but by using strong girders and folding money he had been able to convince them of the soundness of his engineering.

By arrangement, Teal drove up in front of the Bailey residence the morning after their return to town. He improvised on his two-tone horn. Bailey stuck his head out the front door. "Why don’t you use the bell?"

"Too slow," answered Teal cheerfully. "I’m a man of action. Is Mrs. Bailey ready? Ah, there you are, Mrs. Bailey! Welcome home, welcome home. Jump in, we’ve got a surprise for you!"

"You know Teal, my dear," Bailey put in uncomfortably.

Mrs. Bailey sniffed. "I know him. We’ll go in our own car, Homer."

"Certainly, my dear."

"Good idea," Teal agreed; " ’sgot more power than mine; we’ll get there faster. I’ll drive, I knowhe way." He took the keys from Bailey, slid into the driver’s seat, and had the engine started before Mrs. Bailey could rally her forces.