The compound of the snub cube and its dual, the pentagonal icositetrahedron.
Surprisingly, the tribonacci constant is intimately related to the metric properties of the snub cube, its dual, and their compound.
The compound can be constructed from the snub cube with unit edge length by heights and , given by
(1)
 
(2)
 
(3)
 
(4)
 
(5)
 
(6)

where is the tribonacci constant.
The corresponding solid has edge lengths
(7)
 
(8)
 
(9)
 
(10)
 
(11)
 
(12)

The circumradius is given by
(13)
 
(14)
 
(15)

the surface area by the root of
(16)

and volume by
(17)
 
(18)
 
(19)
