Building with PHiZZ unitsand 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

PHiZZ UnitsA PHiZZ unit is a Pentagon-Hexagon Zig-Zag unit.

PHiZZ units become the edges of polyhedra.

These can be used to makeThe dodecahedron (all pentagons) [30 units]Truncated icosahedron (soccer ball) [90 units](Other Buckyballs and Tori)

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

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

PHiZZ unitsWe will make the dodecahedron

Need:30 PHiZZ units……..in 3 colors. (Each table will need to work together)

Steps for folding the PHiZZ unit athttp://www.wikihow.com/Make-a-PHiZZ-Unit

PHiZZ unitsAssembling the dodecahedron Join two units. Then join a third.

Continue. Make pentagons.

Use all 30.

PHiZZ unitsSoftware 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

Small StellaPoly 1.12

More InfoHere at MathFest, the National Association of Math Circles has a table in the Exhibit Hall where they are building models with PHiZZ units.

PHiZZ units

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