The polyhedron compound of the icosidodecahedron and its dual, the rhombic triacontahedron. The compound can be constructed from an icosidodecahedron 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 the largest positive root of
(8)

and volume
(9)
