In an earlier post I implied that I could show the “skeleton” of a rotary 4-cube with just four still pictures of it with its corners lettered A to R (leaving out I and O). This is wrong of course, or incomplete anyway, because there are six different ways in which a 4-cube can execute planar rotation and ought not each to have its own set of pictures?
Thus there are six different sets, each of four parallel, plane faces, about which the 4-cube can pivot. So rather than my measly 4 pictures, actually it would seem to take 6x4 = 24 of them to show the full range of a 4-cube’s rotations from the start through ¼ turn, ½ turn and ¾ turn positions.
By chance, a 4-cube has 24 square faces. Coincidence?
Well, no, not really. Because it wouldn’t need 24 pictures. It would need 6 sets of 4 of them. But the openers of each set would all be the same, namely the starting position. That leaves 24 – 5 = 19 different pictures.
Am I right?
John Scott
johnscott.hyperspace@gmail.com
