Rainbow icosahedron

In this schematic view, the rainbow colors red through purple are labeled 0 through 5. Every possible 3-color combination occurs on exactly one of the 20 triangular faces.

The figure has 3-fold color symmetry: it is invariant under simultaneous rotation through 120° clockwise and addition of 2 (mod 6) to the color labels. The colors on opposite, parallel edges are complementary (labels differ by 3), except on the six bold edges, which demarcate three mutually perpendicular rectangles in 3-space.