Can anyone tell me how to find the number of orbits and number of stabilizers of a dodecahedron without using algebra definitions. I already know the definitions of an orbit and a stabilizer but i don't know what the definitions mean exactly ...
EDIT - Here's the Q i'm trying to answer.
The rotational symmetry group G of a dodecahedron acts transitively on the set of its 20 vertices. The stabilizer of a given vertex is the three rotations (including the identity) about the line through that vertex and the centre. How many rotational symmetries does the dodecahedron have?
Another EDIT! - IS it 3 x 20 = 60? Since #Stab = 3 and #Orbit = 20? Or is it the other way around?