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The point of wearing Tzitzit is for us to remember all of the Mitzvot, (Numbers 15:39) and there are several explanations given for how the Tzitzit remind us of the Mitzvot. However, the explanations given don't seem to account for its required attachment exclusively to a four* cornered garment.

Why do Tzitzit need to be attached specifically to a four cornered garment? What is the four cornered garment's significance?

* Note: Halachically, any garment with four or more corners requires Tzitzit, but the strings are attached to the four corners that are furthest from each other.

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While the garment may have more than four corners, the command is to to put tzitzit on four corners. Rashi connects this to the four expressions of redemption (just like the four cups at the seder).

Rashi says:

on the corners of their garments: Corresponding to [the verse said in connection with the exodus from Egypt]“I carried you on the wings (כַּנְפֵי) of eagles” (Exod. 19:4). On the four corners, but not on a garment of three or five [corners]. [This] corresponds to the four expressions of redemption that were said in Egypt:“I will take you out…I will save you…I will redeem you…I will take you” (Exod. 6:6-7). - [Mid. Aggadah]

Chabad.org points out that

Any garment which has four or more corners is obligated in tzitzit. If the garment has more than four corners, tzitzit fringes are only attached to the four corners furthest from each other

Why Must a Tallit Have Four Fringed Corners? cites Rashi

Rabbi Shlomo Yitzchaki (Rashi) quotes a teaching3 that the corners of the tallit are alluded to in a verse describing the Exodus: “I carried you on the wings (כַּנְפֵי) of eagles.”4 The word kanaf, “wing,” can also mean “corner.” As for why there are specifically four corners, Rashi goes on to explain that they correspond to the four expressions of redemption associated with the Exodus: “I will take you out . . . I will save you . . . I will redeem you . . . I will take you . . .”5

  1. Many say that this teaching comes from Rabbi Moshe Hadarshan, whom Rashi mentions earlier.

  2. Exodus 19:4.

  3. Exodus 6:6–7.

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    +1 Continuing with this theme of redemption, maybe it's possible to say further that it correlates to the "Four corners of the earth" that the Jewish people will be redeemed from? Which would also help explain why if it has more than four corners, you pick the corners that are furthest from each other. Just thinking out loud. – user6618 Apr 15 '16 at 16:18
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    @user6618 , there is indication from the custom to gather up the 4 tzitzis to hold them throughout Shema while saying in the prior berakhah the words, "and You will gather us up from the four corners of the earth". – Micha Berger Apr 15 '16 at 16:24

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