prove that the group of symmetry's of tetrahedron in $R^{3}$ Isomorphic to $S_4$.
2026-04-03 22:42:02.1775256122
prove that the group of symmetry's of tetrahedron in $R^{3}$ Isomorphic to $S_4$.
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Hint: Show that an isometry of the tetrahedron must permute the vertices of the tetrahedron. Show that every permutation of the vertices of a tetrahedron induces exactly one isometry.