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PHiZZ Units (Beauty of Three Dimensional Polyhedra Workshop)


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This is the portion of my workshop on PHiZZ Units (given at MathFest Washington DC 8/7/2015) and some software for investigating polyhedra.
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PHiZZ Units (Beauty of Three Dimensional Polyhedra Workshop)

  1. 1. Building with PHiZZ units and some software for investigating polyhedra PHiZZ Units (#4 of 5) Jim Olsen, Western Illinois University Homepage: ◦ Main webpage: ◦ Main Prezi: ◦
  2. 2. PHiZZ Units A PHiZZ unit is a Pentagon-Hexagon Zig-Zag unit. PHiZZ units become the edges of polyhedra. These can be used to make The dodecahedron (all pentagons) [30 units] Truncated icosahedron (soccer ball) [90 units] (Other Buckyballs and Tori)
  3. 3. Interesting Color Property of the Dodecahedron and Truncated Icosahedron 3 colors (at each vertex) suffice. AND…if you start at one vertex, and make a 2-color path, then the 2-color path visits every vertex once and returns ‘home’ (a Hamiltonian circuit) PHiZZ units
  4. 4. This PHiZZ ball I made for my daughter’s confirmation. It has Bible passages printed on 60 edges (on the Hamiltonian circuit).
  5. 5. PHiZZ units We will make the dodecahedron Need: 30 PHiZZ units…… 3 colors. (Each table will need to work together) Steps for folding the PHiZZ unit at
  6. 6. PHiZZ units Assembling the dodecahedron Join two units. Then join a third. Continue. Make pentagons. Use all 30. 
  7. 7. PHiZZ units Software for investigating polyhedra Poly* & Poly Pro – from Pedagoguery Software (*there is a trial version) They also have a very nice poster. †Quite easy to use. Small Stella*, Great Stella, & Stella4D - from (*there is a trial version) †Full-featured.
  8. 8. Small StellaPoly 1.12
  9. 9. One More Software Package for Visualizing Polyhedra KaleidoTile - Designed to study Tilings and Symmetry (free) – Colorful and good for explorations. from
  10. 10. More Info The National Association of Math Circles uses PHiZZ units. Tom Hull has written a nice book Project Origami: Activities for Exploring Mathematics, Second Edition PHiZZ units
  11. 11. Building with PHiZZ units (Page with Links) (#4 of 5) Jim Olsen, Western Illinois University Homepage: Main webpage: Main Prezi: