Rotational symmertries of octahedron, R($O_3$)
Show that octahedron has 24 rotational symmetries. Show this by showing the automorphisms from R($O_3$) is obtained by which of the eight faces, and how it sends the face with vertices (1,0,0), (0, 1, 0), (0, 0, 1). (please use this method).
Note that the octahedron is on $R^3$ and its vertices are (1,0,0), (0, 1, 0), (0, 0, 1), (-1,0,0), (0, -1, 0), (0, 0, -1).
R($O_3$) denotes the group of rotational symmetries of octahedron.
Sarah M
13
The answer is accepted.
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