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.
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: