The 96 different colorings with two colors for the dodecahedra




Shown are
only 60 patterns. The missing 36 patterns are the complements of the first 36
patterns with less than 6 colored sides. It is remarkable that in the 24
patterns with 6 colored sides a majority (the 12 magenta bordered assymetric
ones, ordered in pairs, and the 4 blue bordered symmetric ones) is equal to their
complement.
Complement
means exchanging colored and uncolored sides.
Counting 2
color patterns on the octahedra gives 23 and on the icosahedra 17’824.
Pink points are behind, the red ones in front.
See the PolyaBurnside Lemma for such countings!
The
PolyaBurnsideFormula for the 2colored dodecahedron is