# Eye-Popping Puzzling Paper-Play

We’re loving the site Papermatrix, where super-talented people show us how to weave paper strips into amazing boxes, balls, and other shapes. And these cool crafts have a ton of math in them. The tube-shaped box shown here repeats 3 diamond shapes, so they almost look like cubes in an optical illusion. It’s made by weaving red upward to the right, blue upward to the left, and yellow down between them. Because of the angles, the blue diamonds look like the tops of cute little cubes, with red and yellow sides. Another project — which they say is easy but takes a bit of time — is a “triacontahedron,” meaning a 30-sided shape! Each diamond-shaped side is made of 4 smaller diamonds. It weaves 6 colors such that the 30 sides mix every possible pair of colors. If you have enough hands and eyes to track all those parts, give it a try!

Wee ones: How many colors can you count on this cube-patterned box?

Little kids: How many rows of “cubes” can you count from top to bottom on the box?  Bonus: If you count 1 cube in each row and each one’s made of 3 diamond shapes, how many diamonds do they have in total?

Big kids: Each blue strip (paired with each red and yellow strip) makes 5 cubes on its way from bottom to top. If the box weaves 14 strips of each color, how many cubes do they make together?  Bonus: For the triacontahedron, how many different pairs of different colors can you choose from 6 colors, ignoring the order?