i saw the figure 5 in gold
yet another duality diagram.
until now, this post from 2010
had my favorite such: “duality in
the fano plane”; seven “lines” through
this one is a much-more-symmetric
picture of the situation represented
in this early version: ten “lines”
through ten points.
it recently occurred to me that
the “desargues configuration”
(aka “the situation represented here”)
could, in some sense, *best* be
visualized as the (set of) *opposite
faces* of an icosahedron.
but before i’d even made a decent
picture of that (hard-to-draw because
3-dimensional), along came this idea.
how it escaped me till now, i’ll never know.