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

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:

• I think the Rambam's case is best understood as weaving more fabric onto the triangle to build it up to a square. (Not that his ruling would or would not apply to your case or other cases.) Commented May 26, 2015 at 2:34
• @DoubleAA Oh... now that makes sense. Commented May 26, 2015 at 3:37
• partial dupe judaism.stackexchange.com/q/26160/759 Commented May 26, 2015 at 13:53
• IIRC, while begadim with MORE than 4 corners DO in fact require tzitzit, it's only required for FOUR of the x corners, not all of them. Commented Jul 27, 2015 at 14:56