He returned in a minute, carrying a very odd-looking thing with him, and set it on the table beside my chair. I examined it for a minute while Farnsworth stood over me, half smiling, his little green eyes wide, sparkling in the flickering light from the fire. I knew he was suppressing his eagerness for my comment, but I was unsure what to say.

The thing appeared simple: a cross-shaped construction of several dozen one-inch cubes, half of them of thin, transparent plastic, the other half made of thin little sheets of aluminum. Each cube was hinged to two others very cunningly and the arrangement of them all was confusing.

Finally, I said, “How many cubes?” I had tried to count them, but kept getting lost.

“Sixty-four,” he said. “I think.”

“You think?”

“Well—” He seemed embarrassed. “At least I made sixty-four cubes, thirty-two of each kind; but somehow I haven’t been able to count them since. They seem to… get lost, or shift around, or something.”

“Oh?” I was becoming interested. “May I pick it up?”

“Certainly,” he said, and I took the affair, which was surprisingly lightweight, in my hands and began folding the cubes around on their hinges. I noticed then that some were open on one side and that certain others would fit into these if their hinging arrangements would allow them to.

I began folding them absently and said, “You could count them by marking them one at a time. With a crayon, for instance.”

“As a matter of fact,” he admitted, blushing again, “I tried that. Didn’t seem to work out. When I finished, I found I had marked six cubes with the number one and on none of them could I find a two or three, although there were two fours, one of them written in reverse and in green.” He hesitated. “I had used a red marking pencil.” I saw him shudder slightly as he said it, although his voice had been casual-sounding enough. “I rubbed the numbers off with a damp cloth and didn’t… try it again.”

“Well,” I said. And then, “What do you call it?”

“A pentaract.”

He sat back down again in his armchair. “Of course, that name really isn’t accurate. I suppose a pentaract should really be a four-dimensional pentagon, and this is meant to be a picture of a five-dimensional cube.”

“A picture?” It didn’t look like a picture to me.

“Well, it couldn’t really have five-dimensionality—length, width, breadth, ifth and oofth—or I don’t think it could.” His voice faltered a little at that. “But it’s supposed to illustrate the layout of an object that did have those.”

“What kind of object would that be?” I looked back at the thing in my lap and was surprised to see that I had folded a good many of the cubes together.