As you may have guessed from the kaleidocycle, I like making geometric shapes out of beads! The first shape I tried was a dodecahedron (or an icosahedron, depending on how you look at it). Here’s a photo of the finished piece.
I made this a few years ago but it’s still one of my favourites. The shape is made up of a lot of individual peyote ovals (like a triangle but with only two points, I learnt about them from Diane Fitzgerald’s book Shaped Beadwork).
If you think of it as a dodecahedron then five of the ovals (or rather, five half-ovals) make up each hexgonal face, while if you think of it as an icosahedron then each oval corresponds to an edge.
Each oval is one of five colours, but they occur in a different order in each hexagonal face. After a bit of reading I found out that this is because the symmetries of a dodecahedron (or icosahedron, they’re essentially the same) are the same as a particular permutation group. (Or in full maths detail: its symmetry group is isomorphic to the alternating group A5, which is the group of all even permutations of a set of 5 elements.) So not only does it look cool it has some pretty neat maths behind it as well!