# Group of Proper Symmetries of Painted Cube

What is the proper symmetry group of a cube in which three faces, coming together at one vertex, are painted green and the other faces are red?

I know that the axis of rotation for which the rotations of $$0$$, $$2\pi/3$$, and $$4\pi/3$$ produce a proper rotational group is $$x=y=z$$ with the intersection points being the intersection of the similarly painted faces. But I'm not sure how to formulate this into a proper symmetry group. Any help would be great, thank you in advance!

• "proper symmetry group" means reflections are excluded? – Parcly Taxel Mar 10 at 5:46
• I think you want the dihedral group of the triangle. – Angela Richardson Mar 10 at 6:03
• Yes, @ParclyTaxel. – James Done Mar 10 at 7:19
• "Proper" has already many meanings, not to be used for another one. "Orientation-preserving", "direct", "group of motions" etc already mean what you want. – YCor Mar 10 at 13:51