Great icosahedron

The great icosahedron, or gike, is one of the four Kepler–Poinsot solids. It has 20 triangles as faces, joining 5 to a vertex in a pentagrammic fashion.

It has the same edges as the small stellated dodecahedron.

Retrosnub tetrahedron
The great icosahedron can also be considered to be a kind of retrosnub tetrahedron, by analogy with the snub cube and snub dodecahedron. It is the result of alternating the vertices of a degenerate uniform polyhedron with 8 degenerate hexagrams and 6 doubled-up squares and then adjusting edge lengths to be equal. It can be represented as s3/2s3/2s.

In vertex figures
The great icosahedron appears as a vertex figure of two Schläfli–Hess polychora.

Related polyhedra
Two uniform polyhedron compounds are composed of great icosahedra:


 * Small retrosnub disoctahedron (2)
 * Small retrosnub icosicosahedron (5)