(R. Yirmeyah mi'Difti): Tana'im argue about Bigdei Kehunah that are too long and were not held up.

(Beraisa #1): "Al Arba Kanfos Kesusecha" excludes a three-cornered garment from Tzitzis.

Suggestion: Perhaps this excludes only a five-cornered garment!

Rejection: "Asher Techaseh Bah" includes a five-cornered garment. Therefore, "Arba" excludes three (-cornered garments).

Question: Why learn this way, and not oppositely?

Answer: A five cornered garment has four corners. A three cornered garment does not.

(Beraisa #2): "Al Arba Kanfos Kesusecha" excludes a three or five-cornered garment from Tzitzis.

Suggestion: The Tana'im argue about whether we ignore something extra.

Rejection: No, all agree that we do not ignore it. The first Tana expounds "Asher Techaseh Bah" to obligate a five-cornered garment

Menachos 28a (Mishnah): The four Tzitzis (sets of strings on each of the four corners of a garment) are Me'akev each other, because they are all one Mitzvah;

R. Yishmael says, each of the four is a Mitzvah by itself.

37b - Question: What do they argue about?

Answer #1 (Rav Yosef): They argue about a linen garment. (If there are wool threads of Techeiles on only some of the corners, the first Tana says that one who wears it transgresses Kilayim.)

Answer #2 (Rava bar Ahina): They disagree about a garment with five (or more) corners.

Answer #3 (Ravina): If there are threads on only some corners, they argue about whether one who wears it in Reshus ha'Rabim on Shabbos is liable.

(Rav Shisha brei d'Rav Idi): If one cut off (on a diagonal) one of the four corners of his garment (this makes it five-cornered), he did nothing.

(Rav Yehudah): The Halachah follows R. Yishmael.

The Halachah does not follow him.

Rif (Hilchos Tzitzis 11a): Chachamim include a five-cornered garment from "Asher Techaseh Bah." R. Shimon learns from "Asher". "Arba" excludes a three-cornered garment.

Rambam (Hilchos Tzitzis 3:3): We include a five-cornered garment and exclude a three cornered garment because a five cornered garment has four corners. Therefore, on a garment of five or more corners, one puts Tzitziyos on the four corners furthest from each other, for it says "Al Arba Kanfos Kesusecha."

Kesef Mishneh: The Rambam reasons that one puts Tzitziyos on the corners furthest from each other.

Rebuttal (Divrei Chamudos on Rosh Hilchos Tzitzis 3, Os 7): The Rambam concludes 'because it says..'! This shows that he learns from the verse. Kenaf" connotes the furthest corner.

Ohr Some'ach: We learn from Zevachim 18b. The Gemara suggested that the Tana'im who argue about a five cornered garment argue also about Bigdei Kehunah that are too long. In Sanhedrin (88b) we say that (if one put extra strings on a corner, if they need not be tied,) each stands by itself, and everyone can see that it is a separate matter. Regarding Bigdei Kehunah, what is past the proper length is clearly extra. R. Yirmeyah surely discusses a parallel case of Tzitzis, in which it is clear which is the extra corner, i.e. it is near another corner. If the corners were equal and it is not clear it is extra, this is unlike Bigdei Kehunah! Rather, he would say that it depends on whether we say that each stands by itself, or if they are considered together, for it is one garment.

Rosh (Hilchos Tzitzis 3): A Sifri learns from "Arba" to exclude a garment of three, five, six, seven or eight corners. It means that had the Torah written only 'Al Kanfei Bigdeihem', we would have thought to make Tzitzis on all corners of the garment, no matter how many there are. "Arba" disqualifies a garment of three corners, even if one attached four (sets of strings). It also teaches that if the garment has five or more corners, one attaches Tzitzis only on four of them.

Shulchan Aruch (OC 10:1): A Talis that does not have four corners is exempt.

Mishnah Berurah (1): A garment without four corners is exempt whether it was initially like this, or if it had four and he rounded one of them.

Kaf ha'Chayim (2): If the garment had four corners, and one of the corners became rounded, it is still obligated. It depends on when the garment was made, like the Shulchan Aruch (11:10) says about Tzitzis put the right distance from the corner, and loater the garment frayed and they are too close.

Shulchan Aruch (ibid): If it has more than four, it is obligated.

Beis Yosef (DH Harei): Chachamim and R. Shimon agree that a five-cornered garment is liable. They argue only about which verse teaches this. The Rif, Rambam, Rosh, Tosfos and Semag say so. Hagahos Maimoniyos (3:2) says that this is unlike the (second) Beraisa in Zevachim, which exempts a five-cornered garment. He says that Tosfos and Sefer ha'Terumah rule like this, and Menachos 37b connotes like this. Re'em and R. Simchah exempt, for they rule like the Sifri and Zevachim against the Gemara in Menachos. Maharik (149) says that this is an individual's opinion, and one may not rely on it at all. Rashi explains that the first Tana in Menachos holds that the four Tzitzis are all one Mitzvah, and the Torah includes a five cornered garment to put Tzitziyos on four corners. R. Yishmael holds that each of the four is a Mitzvah by itself. The Torah includes a five cornered garment to put Tzitziyos on all the corners, for each is a Mitzvah by itself. The Gemara explicitly rules like the first Tana. Also the Rambam rules like this.

Beis Yosef (DH v'Chasuv): The Mordechai (943) says in the name of Tosfos Shantz that since the Gemara mentioned only a garment of five corners, this connotes that a six cornered garment is exempt. However, we obligate a five-cornered garment because it has four corners. Also a garment with six or more corners has four corners! This is astounding. Even without the latter reason, how could we think to distinguish between five and six?! However, l'Halachah he agrees with the Sifri, Rambam, Rosh and Semag that it is obligated.

Taz (1): Perhaps the Torah includes a five cornered garment to put Tzitziyos on all the corners! Also, why do we need "Asher Techaseh Bah" to obligate it? We can learn from reasoning alone (a five-cornered garment has four corners)! The latter question answers the former. "Asher Techaseh Bah" teaches not to say 'since we do not make more than four Tzitziyos, we do not make more than four corners, for corners and Tzitziyos are the same. The extra words include a garment with more corners than Tzitzis. This shows that if there are more than four Tzitziyos, they are Pesulim.

Yad Efrayim: "Al Arba Kanfos Kesusecha" teaches that we put only four Tzitziyos.

Magen Avraham (1): Some exempt a garment with more than four corners, therefore, one should not make a five-cornered garment. Birkas ha'Zevach leans to say like this.

Magen Avraham (2): If one put on five Tzitziyos, he transgressed Bal Tosif (Rashi Devarim 4:2).

Gra (1): The Shulchan Aruch rules unlike R. Simchah, who exempts due to the Beraisa in Zevachim. Also, Menachos 37b says that the Tana'im argue about a five-cornered garment. I.e. Chachamim exempt, and the Halachah follows Chachamim. One who cut his garment did nothing. I.e. he intended to put on Tzitzis, but it is exempt, for now it has five corners. Rashi explains Menachos 37b to obligate a five-cornered garment. Menachos 43b says that Chachamim and R. Shimon both obligate a five-cornered garment, and brings several Beraisos explaining how they could expound "Asher Techaseh Bah." I.e. all of these opinions oppose the Beraisa that exempts a five-cornered garment.

Mishnah Berurah (3): Some exempt a garment with more than four corners, so l'Chatchilah one should not make such a garment. We do not consider a square neck opening of a standard Talis Katan to be four additional (interior) corners, because the majority is closed. If the majority is open, one should make the opening round.

Note - If the majority is open, it is likely that the garment is not considered to be big enough to be obligated, according to the Mishnah Berurah (16:4) who says that the neck opening does not count towards the minimal Shi'ur of an Amah wide and long (or at least three quarters of an Amah long) in front and in back.

Kaf ha'Chayim (1): If the garment has more than four corners, one should not bless on it, for we are lenient about Safek Berachos.

Kaf ha'Chayim (7): If the majority of the garment tore in the middle, it has six corners, and some say that it is exempt, so when one sews it back, he must untie the Tzitziyos and tie them again.

Shulchan Aruch (ibid): One makes four Tzitziyos on the four corners furthest from each other.

Taz (2): It is reasonable to put the Tzitziyos on the four corners furthest from each other, for they are most recognizable.

Gra (DH ha'Meruchakos): The Gemara said 'one who cut his garment did nothing.' If we would not say that he puts the Tzitziyos on the corners furthest from each other, he did something, i.e. he enabled himself to put two of the four Tzitziyos near each other at the cut corner!

Mishnah Berurah (5): Some say that mid'Oraisa one must put on the corners furthest from each other, so one must be stringent about this if possible. If Tzitziyos were already put on a corner not among the furthest from each other and one cannot fix it, e.g. it is time for Tefilah, one may rely on the lenient opinion and bless on it.