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.


Answers can only be viewed under the following conditions:
  1. The questioner was satisfied with and accepted the answer, or
  2. The answer was evaluated as being 100% correct by the judge.
View the answer
The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.