After studying Ariel’s excellent design ideas, Trey shows her the following image:
“This represents what we call a cube,” he says. “It’s like a square, only deeper. The fat red lines are edges that are `nearer’ in the third dimension, while the skinny blue lines are edges that are `farther'”.
“What are the dark diamond shapes in the corners?” Ariel asks.
“Ah, those are edges that go from `near’ to `far’. In my world they are exactly the same as the red edges or the blue edges. People in your world can’t them length-wise, because they extend in that extra dimension that doesn’t exist in your world.”
“Wow!” Ariel says, “I totally get this. And what about the second image I showed Lennie — the diamond shape. In your world, is that just a rotated cube?”
“That’s where it gets weird,” Trey says. “In three dimensions that’s another shape entirely. We call it an octahedron.”
Ariel is fascinated. “Can you show me what an octahedron would look like to me, using this drawing system?”
“Hmm,” Trey says, “let me work on that tonight.”