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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 JR-Olsen@wiu.edu Homepage: ◦ http://faculty.wiu.edu/JR-Olsen/wiu/ Main webpage: ◦ http://wp.me/P6mrPm-E Main Prezi: ◦ http://bit.ly/1Uh8ePp
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……..in 3 colors. (Each table will need to work together) Steps for folding the PHiZZ unit at http://www.wikihow.com/Make-a-PHiZZ-Unit
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 www.peda.com (*there is a trial version) They also have a very nice poster. †Quite easy to use. Small Stella*, Great Stella, & Stella4D - from www.software3d.com (*there is a trial version) †Full-featured. www.software3d.com/StellaManual.php?prod=small
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 http://geometrygames.org/KaleidoTile/index.html
10. 10. More Info The National Association of Math Circles uses PHiZZ units. https://www.mathcircles.org/ 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 JR-Olsen@wiu.edu Homepage: http://faculty.wiu.edu/JR-Olsen/wiu/ Main webpage: http://wp.me/P6mrPm-E Main Prezi: http://bit.ly/1Uh8ePp