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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!

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

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