coloured faces of an octahedron
how many distinct octahedra (all of the same size) are possible if each face of each octahedron is either red, blue or green? the octahedron is a regular solid with 6 vertices, 12 edges and 8 triangular faces.
im having trouble working out how many symmetries there are of an octahedron. 8 faces and 3 colours so different ways to colour the faces would be 8 choose 3 = 56. but obviously 2 ways might have the same physical result if the octahedron was rotated on a vertice, edge or face.