Here's a nice idea for a summer holiday art project, with a mathematical twist: Archimedean graph paper!
What on earth is Archimedean graph paper? It's named after the famous Archimedes (yes, the bathtub guy). Archimedes knew from earlier writers about the famous Platonic solids - the cube, triangular pyramid, octahedron, dodecahedron and icosahedron. These shapes are beautifully symmetric, and all the faces are regular polygons.
Archimedes wrote about ways to take the Platonic solids and turn them into a whole bunch of slightly less symmetric, but even more beautiful shapes which also have regular polygons for faces. Those shapes are called Archimedean polyhedra now. You know some of these shapes - anyone who has looked carefully at a soccer ball, for example, knows what a truncated icosahedron looks like.
If you start with a tesselation instead of a Platonic solid, and do the same tricks Archimedes wrote about, you can get a whole bunch of beautiful tesselations with two or more polygons each. These are called Archimedean tilings. Make graph paper out of one, and you have Archimedean graph paper. Since these patterns are so beautiful, you can use them as the basis for a craft project. This page gives you a few ideas, feel free to leave more ideas in the comments field below!
Drop by the site and download the Archimedean graph paper in the size you want.
Admire the patterns, and experiment with them, thinking how to incorporate them into a piece of art.
After that, it's up to your creativity.
One idea to start with would be to just color them, with pencil, watercolor, textured paint or glitter. Color them according to the symmetries in the pattern - or deliberately clashing with the symmetry.
You could print them onto colored or textured paper, and use it for scrapbooking, combining different patterns and textures together into a larger masterpiece. Imagine a large board, covered in a paper mache of fragments of different patterns - including the archimedean graph papers in different sizes and colors!
A completely different idea would be to cut cookie dough into the squares, hexagons and triangles in your favorite Archimedean tiling. Then the graph paper becomes a guide to help you arrange the cookies on a serving dish!
The last step, of course, is share your work with the world! Take a picture of what you've done, upload it to Pinterest or Instagram or Flickr, and post a link to it amongst the comments below!
These archimedean tesselations can be very beautiful. They're also very mathematical. There's two good reasons to build them into a craft project! I'd love to hear what you do, please post your ideas in the comments below!