A note for day 13 of 2013
How the cube's 13 symmetry planes*
are related to the finite projective plane
of order 3, with 13 points and 13 lines—
For some background, see Cubist Geometries.
* This is not the standard terminology. Most sources count
only the 9 planes fixed pointwise under reflections as
"symmetry planes." This of course obscures the connection
with finite geometry.