Honeycomb Brioche stitch is pretty elastic stitch if you choose the right needle for your yarn. It will be prettier if you make it loose.
This pattern is complete in four rows and you need to cast on even number of stitches including two stitches for edges. In the first and second row you make the pattern and in the third and fourth you offset the pattern. To make it a little easier knit one row with basic stitch. Start the pattern from next row. Always pay attention to right and wrong side of your work. In right side, which that would be row one and row three, you K1b; knit one stitch below. In wrong side, row two and four, you K2tog with with string behind; Knit two stitches together. See below notes for K1b and K2tog.
Cast on:
Even number of stitches (multiple of 2). Knit one row with basic knit stitch, and then start from row 1.
Instruction:
Row 1: Sl1, rep*( k1, k1b), k1 (see note for K1b )
Row 2: Sl1, rep*( K2tog with string behind, K1 )*, K1 (see note for K2tog with string behind )
Row 3: Sl1, rep*( K1b, K1)*, K1
Row 4: Sl1, rep*( K1, K2tog with string behind )*, K1
Note:
k1b (knit one below): Insert the right needle into the stitch below the next stitch from front to back, knit normally and let the stitch above fall from the left needle.
K2tog with back string: Knit the next stitch with the diagonal strand that have been made by knit one below stitch in the previous row. Insert the right needle into the loop/string made by K1b, from front to back, and then pass through the next stitch at the same direction and knit normally.
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