There are a few pictures of truncated icosahedra in the article, alongside several other shapes that are not icosahedra. The point is that they have icosahedral symmetry. The L is important.
This was such a delightful realization I felt the need to comment anyway.
Truncated dodecahedra are made from twelve 10-gon and twenty triangular faces. Truncated icosahedra are made from twenty hexagonal and twelve pentagonal faces.