Like a cube, only deeper

When Tera shows him what she has come up with, Trey is taken aback. “That’s amazing! It just appeared in the air, like a hologram.”

“No biggie — we just call that a picture. Those flat things that you call pictures are so lame.

“Well,” Trey says, “we also have sculpture.”

“True. I didn’t say you were hopeless. Anyway, what do you see?”

“I see two cubes, a fat red one and a skinny blue one, both in the same place. And I totally get that the red one is the one that’s ‘nearer’ in your fourth dimension. But shouldn’t the blue cube be smaller than the red cube, since it’s further away?”

“Ah,” Tera says, “that’s the clever thing about your friend Ariel’s design idea. She doesn’t make things bigger or smaller as they change in that extra dimension. She just makes the lines fatter or skinner — and of course she also uses color. If you make shapes bigger or smaller, which is what most people try to do, it can get a lot harder to see where everything is.”

“Oh, I see,” Trey says, “And the eight little grey cubes are the edges that go from ‘near’ to ‘far’, right? People in my world can only see them on-edge, which is why they look like little cubes.”

“Exactly!” Tera says. “I think you’re getting the hang of this.”

“OK then, what about something diamond shaped?”

“You mean something like your octahedron, but in four dimensions?”

“Yes please.”

“Hmm, I think I can have one ready for you by tomorrow.”

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