Problem 1 (i) Show that all three principal moments of inertia of a solid regular dodecahedron are equal. Hint: you do not need to compute their values. (ii) A rigid body consists of 12 identical thin rods of length a, forming the edges of a cube. Each of the rods has mass m and a uniform mass density. Calculate the moment of inertia tensor of the body.

Problem 1 (i) Show that all three principal moments of inertia of a solid regular dodecahedron are equal. Hint: you do not need to compute their values. (ii) A rigid body consists of 12 identical thin rods of length a, forming the edges of a cube. Each of the rods has mass m and a uniform mass density. Calculate the moment of inertia tensor of the body.