Mathematics Animation: movie of a truncated icosahedron

An icosahedron is a solid with 20 faces each composed of (in a regular icosahedron) equilateral triangles. It has 12 vertices and 30 edges. If each vertex is lopped off then a pentagonal facet appears in place of each vertex and the resulting figure is called a truncated icosahedron. This figure has 32 faces (the 20 of the icosahedron + the 12 pentagons that replace the 12 vertices). The triangular faces of the icosahedron have been converted to hexagons in the process. The truncated icosahedron therefore consists of 12 pentagons (pale blue in this figure) and 20 hexagons (pale purple in this figure). In this animation, the vertices of the mother icosahedron (red) fade in and out to reveal the contained truncated icosahedron. The truncated icosahedron is the underlying arrangement of carbon atoms in C₆₀ or Buckminsterfullerene. See also the animation of Buckminsterfullerene.