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Let C denote the cube . How many rotations are there in which take C to itself?
A. 6; B. 12 C. 18. D. 24
Theorem: A finite subgroup of is one of the following groups:
- : the cyclic group of rotations by multiples of about a line, with k arbitrary
- : the Dihedral group of symmetries of a regular k-gon , with k arbitrary
- the tetrahedral group of 12 rotational symmetries of a tetrahedron;
- : the octahedral group of 24 rotational symmetries of a cube or an octahedron
- : the icosahedral group of 60 rotational symmetries of a dodecahedron or an icosahedron
(courtesy: Tattwamasi Amrutam)