Using only the vertices of a regular icosahedron as the corners, how many equilateral triangles can you make?
What if you could only use the vertices of a regular dodecahedron?
(I) Precisely 40 equilateral triangles could be made using only the vertices of a regular icosahedron as its corners.
(II) Precisely 60 equilateral triangles could be made using only the vertices of a regular dodecahedron as the corners.