This is the portion of my workshop on PHiZZ Units (given at MathFest Washington DC 8/7/2015) and some software for investigating polyhedra. There are additional, associated slideshares.

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. 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. 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. This PHiZZ ball I made for my daughter’s confirmation. It has Bible
passages printed on 60 edges (on the Hamiltonian circuit).

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. PHiZZ units
Assembling the dodecahedron
Join two units. Then join a third.
Continue. Make pentagons.
Use all 30. 

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. Small StellaPoly 1.12

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. 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. 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