Geometry Is Interesting

Geometry is interesting. And mistakes happen.

I have two patterns in the handout for my "Liberating the Labyrinth" class. Debbie New's Unexpected Knitting has beautiful sweater patterns in this technique. The downside from a pedagogical perspective is these are large, complicated sweater patterns. And sweaters need to fit! For the purposes of learning, I thought it would be better to have a couple smaller, easier projects for practice that are good regardless of size. I devised two cube patterns. Each uses 6 modules. That's enough to give the flavor of the technique without overwhelming.

One cube is a zig-zag cube. The pattern is 1 selvedge stitch, decrease (D), increase (I), decrease, increase, decrease, increase, 1 selvedge stitch. The cube is worked back and forth and then seamed. You could also work it in the round. I am pretty sure working DIDIDI or IDIDID doesn't matter. You'll still get a cube. The pattern is commutative. In math, this is when order doesn't make a difference.
10 + 7 = 17 or
7 + 10 = 17.
17 = 17.
You get the same answer.

The other cube uses straight (S) modules as well as decrease (D) and increase (I) modules. This one also makes a cube. What I did not realize, however, is this pattern is not commutative.
24 ÷ 6 = 4 versus
24 ÷ 4 = 6.
4 ≠ 6.
Order matters!

There are 6 potential solutions using a three-unit repeat scheme:

• DISDIS
• DSIDSI
• IDSIDS
• ISDISD
• SDISDI
• SIDSID

I assumed all of them worked. Nope! Geometry is more interesting than that. 

The pattern is worked in the round. I started with Judy's magic cast-on, then flipped it to put the purl ridge on the outside of the work. Doing this creates a zig-zag seam along three edges of the cube. If you pick wisely, the bind-off edge is a zig-zag seam turned 90° on the opposite side of the cube. To make it look really good, work only half the last shaping round, then graft in pattern grafting knitwise in pattern to purlwise. This works on magic numbers divisible by 4.

If the straight module is in the center of each group of three modules, then the whole thing works beautifully. DSIDSI or ISDISD yield exactly what I want.

If the decrease module is in the center of each group of three modules, you still get a cube. However, the final round doesn't match either seam endpoint. You have to break the yarn, join in a new piece of yarn, and seam. IDSIDS or SDISDI are still solutions that produce cubes, but not as elegant.

The one that messed me up is when the increase modules in the in center of each group of three. You would think DISDIS or SIDSID still produce a cube. They can if you don't start with Judy's magic cast-on. If you use the cast-on to avoid seaming, then the starting seam does not join the correct edges. You can't make a cube.

Somehow — I do not remember how — I got the instructions in my handout messed up. How this happened is difficult to remember since I did produce a cube! I may not have written the directions correctly, but I knit the object correctly. Credit to thoppie on Ravelry for catching the mistake.

Because I needed to sit around and knit up samples to figure this out, I made samples on magic number 8 instead of magic number 20. These turned out very cute!

Note: If you are grafting in pattern, I recommend making a provisional graft as I have done in the image. I've used size 10 crochet cotton to sew the graft, including the shaping in pattern. Crochet cotton is easier to pull out if you don't get it correct on the first try. When it was right, then I used duplicate stitch to follow the crochet cotton guideline. Yes, this takes more time. On the other hand, getting the graft right on the first time is worth it, especially if you are working with a lightly-twisted yarn, as I was here.