The polyhedron compound of the truncated icosahedron and its dual, the pentakis dodecahedron. The compound can be constructed from a truncated icosahedron of unit edge length by midpoint augmentation with heights
(1)
 
(2)

The resulting solid has edge lengths
(3)
 
(4)
 
(5)
 
(6)
 
(7)

(8)

surface area given by the fourth largest positive root of
(9)

and volume
(10)
