d4 soccer-ball (football)

The 32-sided Archimedean Solid named "Truncated Icosahedron" is familiar to many from  soccer-balls (a.k.a. association football ball) or even the geodesic domes sometimes called buckyballs.
The Truncated Icosahedron has 12 pentagonal faces and 20 hexagonal faces.
It occured to me that 12 and 20 have a common denominator of "4", so this shape could be used to make a d4 as follows:
label the 12 pentagonal faces "1" through "4" three times
label the 20 hexagonal faces "1" through "4" five times
This creates an equal chace of the die landing on 1, 2, 3, or 4
So I'm offering this "d4 soccerball" die on Shapeways as an alternative d4 shape.