Rhombic Hexecontahedron

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.  

http://www.personal.psu.edu/axd2/quilt/qlt28.html

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.

http://www.janesassaman.com/Jane_Sassaman/home.html 

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.

Such fun!!!