An icosahedron is named after the number of faces that it has.The number of vertices will depend on the exact configuration ofthe shape. For example, a icosahedron in the form of a prism, with18-gons as bases, will have 36 vertices. A pyramid with a 19-gonbase will have 20 vertices. A bipyramid with a decagon base willhave 12 vertices. There are very many more possible shapes.