Does a trapezoid require tzizit? (Or: how to make a four-cornered triangle)

Question

My family was learning Rambam Hilchot Tzitzit 1:16 tonight and had some questions on how this works, as a practical matter:

וכן המטיל לבעלת שלש ואחר כך השלימה לארבע והטיל לרביעית כולה פסולה שנאמר תעשה ולא מן העשוי.

My interpretation: Someone who puts tzitzit on a three-cornered garment, and then completes the fourth: the entire thing is invalid.

We imagined that a three-cornered garment is basically a triangle, like this:

Now, to create a fourth corner, you could fold half of it over and end up with a trapezoid:

In both images, the red dots are where tzitzit would (theoretically) be attached.

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With that introduction, a few questions (sorry).

• Would such a trapezoid be chayav (required) in tzizit?
• If yes, does that mean that any vertex of a polygon with at least 4 sides requires tzitzit?
• If the answer to the above question is no, what kind of vertex does need tzitzit?
• And finally, if we've completely misunderstood the Rambam, how do you turn a triangle into a tzitzit-requiring garment?

Since the post is already full of images, i'll throw in one more: a flowchart to help you understand the questions above:

Answer 1

The Shulchan Aruch in siman 10 siff 5 seems to have learned the gemara the Rambam is based off differently. He assumes we have a basically square material, but only three of the corners are proper corners, the fourth corner is round to a degree that it is not called square for these laws. Then, after affixing the strings the fourth corner is squared off to the right amount.

As far as polygon material goes, from the beginning of that siman, which has it's roots in the gemara and Rambam chapter three, any shape as long as it has at least four corners is required to have tzitzis. The strings should be attached to the corners which are most distant from each other.