Surreptitious quilt puzzles

Friday the 8th at 3:14, I was nabbing a poster from my former office.  I'm mentioned before, I think, that this summer my college is giving employees "off" on Friday afternoons.  This normally doesn't affect me (I do math and such whenever and wherever), but last week I took advantage of the fact that no one would be around to swap some framed art that I do not like from my new office with some posters I'd framed and hung in my administrative office.  

So now the very nice (but not my style) art is in the dean office, and the cheap (but very me) framed poster is in my new office.

I love this poster not just because it has happy colors and is of a quilt, but because it's secretly a math lesson/math puzzle.  Here's the back story.

A quarter of a century ago, I went to a cool and very inspiring math/art talk by a quilter named Margit Echols. Her talk at that conference was about how she'd figured out how to make interlaced, hexagonal weaving patterns in a quilt: the revelation she had was to make a gazillion triangle "blocks" and then sew those together appropriately to make something that looked like an Islamic tiling; just gorgeous.

She also mentioned, as an aside, a "puzzle quilt" she'd designed. Here's how Echols described the math puzzle:

The quilt contains 30 squares that can be matched to make 15 pairs. Each pair is made from a well-known traditional pattern such as Log Cabin, Tumbling Blocks, Snail's Trail, and Monkey Wrench.

Although both squares in a pair are based on the same pattern (that is, the same arrangement of pieces of the same size and shape), the choice of colors and the placement of lights and darks change their appearance so much that they are almost unrecognizable as the same pattern. This is why identical squares often have different names.

Can you match the squares? Example: the squares in the upper left and lower right corners are of identical construction.

I loved this quilt very, very much: I used her idea in my abstract algebra class and in several of my early math/art classes to teach the idea of subgroups within symmetry groups, and students had a lot of fun. I bought a copy of the poster, which I subsequently lost on an airplane (or thought I did; it turns out I'd left it at my sister's house, and two decades later she returned it.)

Echols died not too long after I saw her talk, alas. If you do a web search for her, though, you can still see references to these cool things she's done.