Allison Wang (Truncated icosahedron)

Untitled, folded paper

[32 F, 90 E, 60V] This shape corresponds to the usual system of panels used to make a soccer ball, with every face either a pentagon or hexagon. One result of Euler’s Polyhedron Formula is that every polyhedron that has only pentagonal and hexagonal sides must have exactly twelve pentagons. Can you find and count the twelve pentagons of this model?

The design for this model is due to Tom Hull, who first created the PHiZZ units that make up the structure.