I was inspired by the pictures of the Trekanter pattern, although I’ve not seen the pattern itself and have no idea if my hexagon formula is similar or different:
I started with 20 stitches, and did it all in garter in various Noro yarns.
Here’s each row of a triangle:
1: Either pick up and knit 20, or cast on 20 and knit
2 and every odd row: knit
3: Knit 2 together, knit to last two stitches, knit 2 together (18 stitches)
5: Repeat row 3 (16 stitches)
9: Repeat row 3 (14 stitches)
11: Repeat row 3 (12 stitches)
15: Repeat row 3 (10 stitches)
17: Repeat row 3 (8 stitches)
21: Repeat row 3 (6 stitches)
23: Repeat row 3 (4 stitches)
27: knit 2 together twice (2 stitches)
29: Knit two together (1 stitch)
Use this one stitch as the start, and pick up 19 more down the left side of the triangle, that is a new row 1. (Otherwise, if you prefer, just bind off and pick up 20 stitches somewhere else.)
When you are finishing a hexagon (starting the sixth triangle around a single point), each time you get to the end of an odd row, knit the last stitch together with one stitch from the adjacent triangle, so that you are knitting the hexagon together when you finish this last triangle. If you don’t mind sewing, you can always simply finish your triangle regularly, and then sew it to close the hexagon.
I mostly just kept going left, but there were times when I finished a circuit, and then had to pick up somewhere else, so I varied a little in how I went. After I saw how the colors were working out, I paid a little more attention to get a light side/dark side effect as well.
I marked the center of the first hexagon, and then kept going until I counted 4 more layers out from each point of that first hexagon.
Since I didn’t want an edging that would fight with the colors, I did a simple single crochet around the edge.