—And He Built a Crooked House

One of the great science fiction short classics is Heinlein’s “—And He Built a Crooked House,” in which a character builds a house in the shape of an unfolded four-dimensional hypercube or tesseract (I’ve always wanted one like it):

Just as a cube folds out into six squares, a tesseract folds out into eight cubes. Now this makes for an interesting house design, but even more interesting is that, during an earthquake, the house “folds up” in the fourth dimension. Which is hard to picture. This is one view, which gets the connections between the eight cubes right, but ignores the fact that they all have the same size and shape:

In Heinlein’s words:

‘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 not square, 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.’

Here is another view (on second thoughts, maybe living in a house like that would make me sea-sick):