[For this problem, refer to the parenthetical statement at the end of 57.12, and itsaccompanying figure. Also see the instructions for 8.17.] The group of all rotationsof a regular tetrahedron has order 12.(a) Find the permutation of the vertices corresponding to each of the eight 1200 rotations aboutlines such as ae.(b) Find the permutation of the vertices corresponding to each of the three 1800 rotations aboutlines such as fg.(c) Show that each permutation of the vertices corresponding to a rotation of the group is aneven permutation (Section 7).

L32 - 4 Evaluating Deﬁnite Integrals as Signed Area ▯ 6 ex....