Calculate the orders of the following (refer to Figure 27.5 for illustrations). a....

Calculate the orders of the following (refer to Figure 27.5 for illustrations).

a. The group of rotations of a regular tetrahedron (a solid with four congruent equilateral triangles as faces)

b. The group of rotations of a regular octahedron (a solid with eight congruent equilateral triangles as faces)

c. The group of rotations of a regular dodecahedron (a solid with 12 congruent regular pentagons as faces)

d. The group of rotations of a regular icosahedron (a solid with 20 congruent equilateral triangles as faces)