Coloring of Archimedean solids

[Sebelev]

Hello!
I began to notice that when choosing a subsymmetry in Archimedean solids, the initial coloring of the polyhedron changes. That is, for example, a cuboctahedron, it has red squares and yellow triangles, but when choosing, let's assume a tetrahedral subsymmetry, and then the octahedral (that is, the initial) squares become yellow, and the triangles become red. Is this a mistake?

[robertw]

Nope, not a mistake. The model is recoloured according to the new symmetry. It means that under tetrahedral symmetry, not all squares can be transformed to align with all the other squares.

If you want to maintain the initial colouring though, you can disable "Options->Recolor Sub-symmetries" before changing the symmetry group.

[Sebelev]

Sorry, I didn't explain it correctly. After switching from tetrahedral to octahedral symmetry it loses its original coloring (Initial - ˃ Any other - ˃ Initial).

Another example: Rhombicuboctahedron. In the initial coloring the first type of faces (squares) are red, the second (also squares) are yellow, and the third (triangles) are blue. But when changing the symmetry and then returning to the initial one (that is, octahedral for the rhombicuboctahedron), the first type of faces becomes yellow, the second - blue, and the third - red, which is illogical given the order of colors in your Software. I understand that when choosing another symmetry, the polyhedron is recolored in accordance with the selected symmetry, but when returning to the initial one, it again does not retain its coloring, but it should.

[robertw]

Ah sorry, I see. Hmm, is it important? I'm not sure why it ends up different, just something being done in a different order, but it does end up with a valid colouring. There's nothing really "correct" about the original colouring. When changing back to the original symmetry, it's kind of free to decide what order to colour the different face types.

[Sebelev]

Okay, thanks. I was just curious.