### Spring 2018 Origami Final Projects

Here are the final projects completed for MATH 2890 and 3890, Mathematics and Origami, in Spring 2018.
• Johnson solids, created by Jonathan McGill from business cards (see [3]).
• Menger sponge, front view and side view, created from over 2400 business cards by Logan Biggins, Layne Kisling, and Olivia Long (see [3]).
• Truncated Icosahedron created by the PHiZZ unit, created by Travis Amerine, Connor McAllister, and Caleb Smith, in five colors using a symmetric color scheme (see [3]).
• Another Truncated Icosahedron, this one created using a flat unit designed by James Plank in two colors, created by Lisa Dewen, Tucker Feix, and Emma Kunard (see [5]).
• Dodecahedral assembly created from the Snow-Capped Sonobe module by Sydney Cannon. Sydney designed the color scheme and created the paper that is white on one side and colored on the other using a spreadsheet and a color laser printer (see [4]).
• Torus, created using 84 copies of the PHiZZ unit, in two colors, by Alex Ott and Luke Vaughan. The unit has faces consisting of eight pentagons, sixteen hexagons, and four octagons (see [3]).
• Truncated Tetrahedron, Truncated Octahedron, and another Truncated Icosahedron, created using the triangular vertex module of B. Arnstein by L. Mantini. These models are all symmetrically colored. The truncated tetrahedron and truncated octahedron are colored in four colors, and the truncated icosahedron in five colors (see [2]).
• Cuboctahedron, created using a module inspired by J. Plank's Penultimate Polyedra modules by L. Mantini. This is a symmetric coloring in four colors.

### Sources Consulted for Origami Models

Here are the sources consulted for the origami models seen above.
1. T. Fuse, Unit Origami: Multidimensional Transformations, Japan Publications, 1990.
2. R. Gurkewitz and B. Arnstein, 3-D Geometric Origami: Modular Polyhedra, Dover Publications, 1996.
3. T. Hull, Project Origami: Activities for Exploring Mathematics, second edition, A.K. Peters, 2012.
4. M. Mukerji, Marvelous Modular Origami, A. K. Peters, 2007.
5. J. Plank, Penultimate Polyhedra, preprint, downloaded from http://web.eecs.utk.edu/~plank/plank/origami/poly.pdf.

Lisa A. Mantini