Do you enjoy math? I hope so! If not, browsing this post just may change your mind. Welcome to the ** Math Teachers At Play** blog carnival — a smorgasbord of ideas for learning, teaching, and playing around with math from preschool to pre-college.

Let the mathematical fun begin!

## POLYHEDRON PUZZLE

By tradition, we start the carnival with a puzzle in honor of our 62nd edition:

An Archimedean solid is a polyhedron made of two or more types of regular polygons meeting in identical vertices. A rhombicosidodecahedron (see image above) has 62 sides: triangles, squares, and pentagons.

How many of each shape does it take to make a rhombicosidodecahedron?My math club students had fun with a Polyhedra Construction Kit. Here’s how to make your own:

- Collect a bunch of empty cereal boxes. Cut the boxes open to make big sheets of cardboard.
- Print out the template page (→) and laminate. Cut out each polygon shape, being sure to include the tabs on the sides.
- Turn your cardboard brown-side-up and trace around the templates, making several copies of each polygon. I recommend 20 each of the pentagon and hexagon, 40 each of the triangle and square.
- Draw the dark outline of each polygon with a ballpoint pen, pressing hard to score the cardboard so the tabs will bend easily.
- Cut out the shapes, being careful around the tabs.
- Use small rubber bands to connect the tabs. Each rubber band will hold two tabs together, forming one edge of a polyhedron.
So, for instance, it takes six squares and twelve rubber bands to make a cube. How many different polyhedra (plural of polyhedron) will you make?

Can you build a rhombicosidodecahedron?

And now, on to the main attraction: the 62 blog posts. Many of the following articles were submitted by their authors; others were drawn from the immense backlog in my blog reader. If you’d like to skip directly to your area of interest, here’s a quick Table of Contents: