Nobody has mentioned (or discovered?) the fully-interlocked
checkerboard pattern obtained by applying the Pons Asinorum
transformation to the Plummer's Cross as suggested
by Greenberg during his description thereof, and then performing
a few triple-center swaps (unfortunately, I was playing rather randomly
with the 3c swaps at the time and must leave them as an "exercise for
the reader"). The six colors are interlocked in pairs of AB, BC, CD, DE,
EF, and FA on each checkerboard. Quite mysterious.