I embarked on an adventure. First I tried to knit a lacy strap that was k2tog yo but it twisted in a corkscrew fashion. So I went to the stitch dictionary and found a different stitch pattern called woven stitch, which is as follows:
Cast on multiple of 4.
Row 1 & 3: purl
Row 2: k2 PT
Row 4:PT k2
Row 1 & 3: purl
Row 2: k2 PT
Row 4:PT k2
Where PT is purl twist. This means that you purl 2 together, leave on the left needle, insert right needle between the stitches from the back and purl the first stitch again.
Knit for 64 inches or so. To make the smaller loops at either end of the strap, when you reach 4” or so, fold the strap up and pick up the cast on stitches on a 3rd needle, purl together on a purl row. This should give you a loop about as wide as the strap itself is. Continue knitting. When your strap is long enough, fold the end up so that you have a similar sized loop, pick up stitches on a 3rd needle and do a 3 needle bind off.
Now comes the origami portion of our adventure. To made the big loops for the mat to rest in, you pass one end through the small loop on the other end. Then you pass the end that has been looped through the small loop on the other end. I found the method on this blog.
For my strap I cast on 14 stitches, I added a purl stitch to either side of my 12 stitch repeat. I also slipped the first stitch of each row with the yarn in front.