I was recently chatting with an experienced teacher who pointed out that playing with Geometiles would be an excellent way for students to transition into being in a classroom. That idea stuck with me, and I experimented with taking it literally. What if we make ice cube models with Geometiles? Then Geometiles “icebreakers” would be taking them apart and putting them together. And since many people’s summers involve ice, the Geometiles ice cubes would literally be the point of transition from Summer (chilling with an iced drink) to Fall (breaking the ice with a classmates).

During the Labor Day holiday, which tends to mark the end of summer, I came up with a puzzle. The Geometiles “ice cubes” are simply cubes made with 6 white and 6 blue right isosceles triangles. There are many ways to arrange the white and blue pieces, and one way to classify them is as follows.

We’ll say that two triangles **SHARE AN EDGE** if they are snapped together along that edge. For example, the white tile on the top face of the cube below shares two of its edges with blue tiles and one edge with a whilte tile.

Now here is the puzzle:

- Can you construct a cube so that each triangle shares every edge only with triangles of different colors?
- Can you construct a cube so that each triangle shares exactly ONE edge with a triangle of a different color?
- Can you construct a cube so that each triangle shares exactly TWO edges with a triangle of a different color?

I will continue playing around with this puzzle, and I hope you do too!

Need some isosceles triangles to try this out with? You will need 12 of them, equally split among two colors. Here are some options.

4&More Isosceles Set has 24 isosceles triangles, enough for two separate puzzles.

Another option is two Mini3 Sets— they contain other shapes for different explorations.

The blue and white ones are part of our Red White & Blue Jumbo set.

Want to explore more activities with isosceles triangles? Check out our ISOsolids activity book.