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 17824.

Pink points are behind, the red ones in front.

See the Polya-Burnside Lemma for such countings!

The Polya-Burnside-Formula for the 2-colored dodecahedron is

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