I want to create a faceted checkered sphere (much along the lines of the
Amiga "Boing!" ball).

To do this I figure I'd take a sphere, build a several rings of boxes (one
for each vertical level of facets, eight I guess), each ring rotationally
staggered from the one above/below (I figure seven boxes per ring, so each
staggered ring would be rotated along the vertical axis by 1/14th of a full
rotation), and then this superstructure would be merged together, given one
set of attributes to cut into the sphere with, spun 1/14th a turn, and cut
again with another set of attributes.

I could be pretty far ahead of myself here though, as I don't really know
how to do any of that. :-)

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