Icosahedron

The icosahedron, or ike, is one of the five Platonic solids. It has 20 triangles as faces, joining 5 to a vertex.

It is the only Platonic solid that does not appear as a cell in one of the convex regular polychora.

Vertex coordinates
The vertices of an icosahedron of edge length 1, centered at the origin, are all cyclic permutations of


 * (0, ±1/2, ±($\sqrt{10+2√5}$+1)/4).

Snub tetrahedron
The icosahedron can also be considered to be a kind of snub tetrahedron, by analogy with the snub cube and snub dodecahedron. It is the result of alternating the vertices of a truncated octahedron and then adjusting edge lengths to be equal. It can be represented as s3s3s.