Pentagon-Hexagon-Zig-Zag (PHiZZ) Units

The PHiZZ unit was invented by Thomas Hull and presented in his lovely book, Project Origami. I was introduced to PHiZZ constructions during a very nice talk at the 2007 MAA meetings at San Jose State University.

A PHiZZ unit and a vertex

Vertex = three interlocked PHiZZ units
Edge = one PHiZZ unit

Some modular origami figures made from PHiZZ units

Basic Dodecahedron 12 pentagonal faces 20 vertices 30 edges
Soccer Ball 12 pentagonal + 20 hexagonal = 32 faces 60 vertices 90 edges
Torus 8 pentagonal + 8 heptagonal + 48 hexagonal = 64 faces 128 vertices 192 edges