 |  |
The pentakis
dodecahedron is the 60-faced dual polyhedron of
the truncated icosahedron 
(Holden 1971, p. 55). It is Wenninger dual 
. It can be constructed by augmentation
of a unit edge-length dodecahedron by a pyramid
with height 
.
A tetrahedron 10-compound, cube 5-compound, icosahedron, and dodecahedron can be inscribed in the vertices of the pentakis dodecahedron (E. Weisstein, Dec. 25-27, 2009).
The pentakis dodecahedron is he convex hull of the small triambic icosahedron hull.
Taking the dual of a truncated icosahedron with unit edge lengths gives a pentakis dodecahedron with edge lengths
 |  |  |
(1)
|
 |  |  |
(2)
|
Normalizing so that 
, the surface area and
volume are
 |  |  |
(3)
|
 |  |  |
(4)
|
