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

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

(7)

surface area given by a root of a 32nd order polynomial with large integer coefficients, and volume
(8)
