# Great icosahedron

The great icosahedron can be constructed analogously to the pentagram, its two-dimensional analogue, via the extension of the (*n-1*)-D simplex faces of the core *n*D polytope (equilateral triangles for the great icosahedron, and line segments for the pentagram) until the figure regains regular faces. The grand 600-cell can be seen as its four-dimensional analogue using the same process.

The *great icosahedron* can be constructed a uniform snub, with different colored faces and only tetrahedral symmetry: . This construction can be called a *retrosnub tetrahedron* or *retrosnub tetratetrahedron*,^{[1]} similar to the snub tetrahedron symmetry of the icosahedron, as a partial faceting of the truncated octahedron (or *omnitruncated tetrahedron*): . It can also be constructed with 2 colors of triangles and pyritohedral symmetry as, or , and is called a *retrosnub octahedron*.

It shares the same vertex arrangement as the regular convex icosahedron. It also shares the same edge arrangement as the small stellated dodecahedron.

A truncation operation, repeatedly applied to the great icosahedron, produces a sequence of uniform polyhedra. Truncating edges down to points produces the great icosidodecahedron as a rectified great icosahedron. The process completes as a birectification, reducing the original faces down to points, and producing the great stellated dodecahedron.