For the symmetries of the equilateral triangle, we let ρ denote the rotation by 120 degrees, and let f be the flip over one of the axes of the triangle. If we allow inverses as well, we...For the symmetries of the equilateral triangle, we let ρ denote the rotation by 120 degrees, and let f be the flip over one of the axes of the triangle. If we allow inverses as well, we can then get every element of the group from a single generator: the inverse of 1 is −1, so we can write (for example) −4=(−1)+(−1)+(−1)+(−1). (Including the inverses also means we don't need to include the identity, since for any g, gg−1=e.)
