Overview: Students piece together twenty slotted equilateral triangles cut from card stock to make a ball. Here's what the ball looks like:
There are a few interesting things about this construction, and depending on time the facilitator can reveal these things more or less gradually. I didn't have confidence in my students' attention span, and so started on the multi-color construction.
I printed the templates on five colors of Wasau Astrobrights cardstock. Construction calls for four triangles of each color. The template prints eight to a sheet, so I precut them into halves. Students had to further cut into triangles and cut the slots. The slots are how the triangles are pieced together.
Next, students need to explore and figure out how the triangles slide together to form a stable shape. Prompts are: make a natural structure with the triangles, use the slots, structure should be three-dimensional, pieces should not be bent or folded, structure should be symmetric, and should use all twenty triangles.
Here's an example of the basic shape. Notice that five triangles combine to form a pentagonal hole.
Once students have this basic shape, it's a matter of extending around in a ball.
Once they built the ball, I then asked them to take it apart and rebuild it. This time they should make sure each pentagonal hole was surrounded by each of the five colors. About half the class was unwilling to do this. But the other half accepted the challenge and accomplished it, one staying after the bell to complete her project.
Some interesting things: A cube is visible embedded in the ball. There appear to be only four unique ways to assemble the ball with five colors to a pentagonal hole. The figure can be thought of as an icosahedron whose faces are rotated. Positioning five colors around a hole gives to opportunity to discuss permutations involving circles.
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