Ladders meet slip and hold, go around to form new shapes

The concept for this post began in 2022, and as so often happens, I got distracted by some other rabbit hole and came across its draft while looking for another previous post.
In November 2025, a similar approach was used to produce modified hexagons to achieve automated star shapes.
The basic steps
1: Put in hold the number of needles planned for the radius, cast on with waste yarn, and knit several rows in the planned needle arrangement.
2: Set the knit carriage for plain knit and holding, and with the project yarn, knit one row.
The outer edge of the final shape will be on the side opposite the starting side, where only one row is knit across all needles in work before short rows start.
The remaining rows are worked in pairs, bringing needles first out of and later back into work position, and when the desired number of segments is reached, knitting ends with a single knit row as well.
Visualizing composing a variety of geometric shapes, and with the addition of ladders and increasing numbers of segments to form shapes other than larger triangles,which requires some practice and patience. The printed 64-row repeat chart can prove useful in tracking the required hand techniques. It is intended to be followed with the first row executed from left to right, and then with holding pairs of rows from right to left. The chart can be mirrored horizontally and followed for operating from the opposite side. Grey cells represent needles out of work forming ladders and eyelets. Eight segments form a square with sides that, depending on yarn choice, may bow toward its center and move away from straight lines.
Although the small ladder spaces add interest, they add tracking complexity in knitting and can be eliminated.
A yarn that can be blocked flat is a better choice than one that will spring back at the edges and curl.
Omitting the smaller shapes, in the bottom angle, as stitches are brought out to hold, to maintain a constant 4 needles in work, bring an empty needle into work on the left, and transfer a stitch on the needle to the right, with the last transfer on row 17.
To make a sharper turning point, 4 rows rather than 2 on single stitches could be considered before the return needles to work sequences.
On row 38, transfer stitch to the left, taking the needle out of work, forming a ladder. Repeat until 3 empty needles are reached, and maintain the ladder space size by transferring a stitch to the left, bringing an empty needle back into work on the right until the starting needle arrangement is reached, then reverse shaping.
To bind off, take off on waste yarn, rehang stitches, knit side facing, for both bottom and top edges, use your preferred bind off.
Steaming at least the top and bottom of the swatch before joining to make the stitches more visible when picking up may be helpful. I did not. Other bind-offs, including grafting, may improve the join.
Triangular versions in differnt color and yarn choices, and an attempt at going square. In a last try at forming a square, the new, taller repeat has more constant stitch counts, making transfers and held stitches easier to ID.
The yarn used is a wool rayon, knit at tension 6, resulting in very small stitches around the outer edge, even with the use of weight on that side. This would become a consideration if one chooses to block the individual results or when joining multiple pieces together.
The revised 70-row repeat chart can be printed and marked as desired.This swatch was the first ever that I blocked to coax a more permanent, final square shape, using ribber comb wires. The base is an old, bulky felted swatch, my go-to when steaming/ pressing swatches. The result after resting, perhaps needing a few more small tweaks.