Some Solid Connections, Page 4: The Icosadodecahedron

Taking this investigation to the next pair of dual platonic solids, here is the bisected-edge truncation of the icosahedron:

The bisected-edge truncation of the Dodecahedron:

Similar to the case above (with the cube and octahedron), the bisected-edge truncations of the icosahedron and dodecahedron produce the same solid: the icosidodecahedron.

Therefore, it can be seen the icosahedron and dodecahedron are duals:

Now, the symmetry of the the spherical arcs from the icosahedron, dodecahedron, and the icosidodecahedron mapped on the same sphere: