**Project Idea:** Make a Hexaflexagon

First, it seems prudent to introduce the concept of a “flexagon” itself. According to Wikipedia, flexagons are, “…flat models… that can be *flexed* or folded in certain ways to reveal faces besides the two that were originally on the back and front.” The hexaflexagons we’re interested in are actually trihexaflexagons- named as such due to their three faces and six sides.

There is a paper titled “Hexaflexagons and the Other Feynman Diagrams,” that goes into some of the mathematical properties of hexaflexagons and the different ways they have been diagrammed.

We were thinking of using fabric and a sewing machine to make a hexaflexagon. This website has a detailed explanation of how to make one. The process could also be adapted to make a double hexaflexagon.

**Project Idea:** Put mirrors inside of polyhedra

Putting mirrors inside polyhedra creates a kaleidoscope. This project could involve studying how mirrors reflect light at different angles and how that results in a kaleidoscope. This article explains some of this math.

The simplest way to actualize this idea is by using the Geometiles mathematical toys. These are polygonal tiles that can be snapped together to create larger mathematical objects, and are simple enough to glue mirrors into. (In fact, they plug the method on their website for smaller polyhedra, making simple kaleidoscopes!)

LEDs can also be added to the polyhedra to make it looks extra cool like this.

**Project Idea**: Make playing cards, where each is illustrated

with an example of something from a set of size

52 or from four sets of size 13. This project could be thought of combinatorially. The math part of this project could be coming up with different sets of size 52, using the choose function. Combinatorics and decks of cards are extremely linked. This article discusses some of the combinatorial card problems. The making process for this project wouldn’t be very difficult- at the most basic level, you could take paper and cut it into 52 equal-sized pieces, or paint over an existing set of cards. Or use notecards. Notecards work too. Once you had your cards of choice, you could draw or print designs on them as you wished.

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