- In the plane, exactly six equilateral triangles fit together at each point.
Use equilateral triangles to construct a model of space where only five equilateral triangles meet at each point. Continue the model as far as you can. That is, once you have 5 triangles meeting at the center of one disc, move to the edge of that disc and add triangles until there are five meeting at that vertex as well. Then move further out on your surface, making sure that 5 triangles meet at each vertex. OR - Using playdough, form a disc. Find a way to decrease the circumference without changing the diameter. Do not tear the disc.
- Use equilateral triangles to construct a model of space where seven equilateral triangles meet at each point. Again, continue the model as far as you can, making sure that 7 triangles meet at each vertex.
Once you've used up all your triangles, join your construction to someone else's (still making sure that 7 triangles meet at each vertex).
OR
- Using playdough, form a disc again. This time, find a way to increase the circumference of the disc without changing the diameter, and again, without tearing the disc.