Well, obviously there's a fair amount of math and geometry involved in quilt patterns. But what happens when an actual mathematician is also a quilter? A friend sent me a link to such a person's website. One of the things she played around with is a rhombic hexecontahedron. Yup.
A rhombic hexecontahedron seems to me very closely related to a dodecahedron. That's one of the Platonic solids, made famous (to me anyway) in the book "The Phantom Tollbooth", written by Norton Juster, illustrated by Jules Feiffer. This is one of my all-time top favorite books, nominally a children's book, but a great read at any age.
Both shapes have 12 faces. The dodecahedron usually has pentagonal faces, but the rhombic hexecontahedron goes one step further by using 5 diamonds to make concave and pointy-edged faces. Well, for some reason, I've always found the dodecahedron a very pleasing shape. Maybe because I like "The Phantom Tollbooth" so much. Also because it's such a fun word to say. The rhombic hexecontahedron is harder to say, but is a more graceful and interesting version of a dodecahedron. So I decided to make one, too.
One of the suggestions on the math/quilt page was to fussy cut print fabrics in each star-shaped side. (Fussy cutting means cutting the shapes precisely according to the print.) I decided to use fabrics from Jane Sassaman's great collection. Wonderful bold colors and interesting stylized designs.
My rhombic hexecontahedron is about 6" tall. I followed the process described on that webpage: cardboard diamonds, aka rhombuses, covered with batting, covered with the fabric, then stitched together. The diamonds are almost the 60-degree diamonds used in Grandmother's Flower Garden and such quilts. But officially, they are supposed to be 63-degree diamonds, in which some of the dimensions end up in the Golden Ratio. (I couldn't possibly explain that concept, but recommend another book - "The Golden Ratio: The Story of Phi, The World's Most Astonishing Number" by Mario Livio. It's written for non-mathematicians, a fascinating read.) Because there are 5 diamonds, instead of 6 like a quilt would have, they automatically go concave, to just the right angle.