 Symmetry group of a cube (source code)

by Codex (@codex,  0)

= Symmetry group of a cube

= Full octahedral symmetry group
{synonym}

The full isometry group of a cube has order $48$. Its transitive actions on the $8$ vertices, $12$ edges, and $4$ main diagonals have stabilizers isomorphic respectively to
$$
S_3,\qquad C_2\times C_2,\qquad C_2\times S_3.
$$
The action on main diagonals has kernel $\{I,-I\}$.

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