Affine-Regular 120-Cells

Anyone who has built a 120-cell (hyper-dodecahedron) model with Zome knows that it contains several kinds of "squashed" dodecahedra, in addition on one regular blue dodecahedron in the center. There are two kinds of "squashings" along a red axis, and one along a yellow axis. Each of these corresponds to an affine transformation in the Zome vector space, and that transformation can be applied uniformly to any vZome-constructible object. Furthermore, its inverse can be applied as well.

If we designate the kinds of dodecahedral cells as "red-1", "red-2", "yellow-1", and "red/yellow-0" (where the latter refers to the central dodecahedron), we can enumerate eight different affine transformations with a simple nomenclature: color-M-N means that cell "color-M" is transformed into cell "color-N".

Each of the eight possible affine transformations is illustrated below, applied to a 120-cell. Of course, there are an infinite number of affine transformations possible, but these eight have the advantage of introducing a minimum number of non-rZome edges; in some cases, as you'll see, there is only one non-rZome color required.

For each of the triplets of images below, the left-hand pair form a "wall-eyed" stereo pair, and the right-hand pair form a "cross-eyed" pair. Also, you can click on any image to load the model in vZome, using Java Web Start.

red-0-1

red-1-0

red-0-2

red-2-0

red-1-2

red-2-1

yellow-0-1

yellow-1-0