Use the counting formula to determine the orders of the grou

Use the counting formula to determine the orders of the groups of rotational symmetries of a cube and of a tetrahedron.

Solution

solution -: As stated in the problem (and as we can check by drawing it), there are exactly two
ways to inscribe a regular tetrahedron in a cube. If we denote one such tetrahedron
by delta , we thus have |O| = 2. , the order of rotational symmetries of a
cube is 24. By the counting formula, we have |Stab delta|= 24/2 = 12.