One way to construct a great dodecahedron is by faceting the regular icosahedron.

In other words, it is constructed from the regular icosahedron by removing its polygonal faces without changing or creating new vertices.

The construction started from a regular dodecahedron by attaching 12 pentagonal pyramids onto each of its faces, known as the first stellation.

Historically, the great dodecahedron is one of two solids discovered by Louis Poinsot in 1810, with some people named it after him, Poinsot solid.

As for the background, Poinsot rediscovered two other solids that were already discovered by Johannes Kepler—the small stellated dodecahedron and the great stellated dodecahedron.

[3] However, the great dodecahedron appeared in the 1568 Perspectiva Corporum Regularium by Wenzel Jamnitzer, although its drawing is somewhat similar.

[5] The great dodecahedron appeared in popular culture and toys.

A truncation process applied to the great dodecahedron produces a series of nonconvex uniform polyhedra.

Truncating edges down to points produces the dodecadodecahedron as a rectified great dodecahedron.

The process completes as a birectification, reducing the original faces down to points, and producing the small stellated dodecahedron.

It shares the same edge arrangement as the convex regular icosahedron; the compound with both is the small complex icosidodecahedron.