“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 do all 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 — “