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The great dodecahedron is the Kepler-Poinsot polyhedron whose dual is the small
stellated dodecahedron. It is also uniform
polyhedron with Maeder index 35 (Maeder 1997), Wenninger index 21 (Wenninger
1989), Coxeter index 44 (Coxeter et al. 1954), and Har'El index 40 (Har'El
1993). Its Schläfli symbol is 
and its Wythoff symbol
is 
.
It consists of 12 intersecting pentagonal faces (
).
The great dodecahedron is implemented in the Wolfram Language as UniformPolyhedron[21],
UniformPolyhedron["GreatDodecahedron"],
UniformPolyhedron[
"Coxeter", 44
], UniformPolyhedron[
"Kaleido", 40
], UniformPolyhedron[
"Uniform", 35
], or UniformPolyhedron[
"Wenninger", 21
]. It is also implemented in the Wolfram
Language as PolyhedronData["GreatDodecahedron"].
Schläfli (1901, p. 134) did not recognize the great dodecahedron as a regular solid because it violates the polyhedral formula, instead satisfying
 |
(1)
|
where 
is the number of vertices, 
the number of edges, and 
the number of faces (Coxeter 1973, p. 172).
The skeleton of the great dodecahedron is isomorphic to the icosahedral graph.
The 12 pentagonal faces can be constructing from an icosahedron by finding the 12 sets five vertices that are coplanar and connecting each set to
form a pentagon. A version split along face intersections can be constructed by augmentation of a unit edge-length icosahedron
by a pyramid with height 
. This gives side of lengths
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
where 
is the golden ratio.
Its circumradius for unit edge length is
 |  |  |
(5)
|
 |  |  |
(6)
|
where 
is the golden ratio.
The resulting solid has surface area and volume
 |  |  |
(7)
|
 |  |  |
(8)
|
The convex hull of the great dodecahedron is a regular icosahedron and the dual of the icosahedron is the dodecahedron, so the dual of the great dodecahedron (the small stellated dodecahedron) is one of the dodecahedron stellations (Wenninger 1983, pp. 35 and 40)
." §3.6.2 in