If the number of corners on a garment is a multiple of 4, such as 8, does the garment require tzitzit for more than the 4 outermost corners?
While not exactly explicit, Maimonides (Tzitzith 3:3), based on the baraita cited in the Talmud (Menachoth 43b), codifies that only the four outermost corners of a multi-cornered garment require tzitzith, without any disclaimer regarding garments that have eight or more corners:
(דברים כב יב) ״עַל אַרְבַּע כַּנְפוֹת כְּסוּתְךָ״ בַּעֲלַת אַרְבַּע וְלֹא בַּעֲלַת שָׁלֹשׁ. אִם כֵּן בַּעֲלַת אַרְבַּע וְלֹא בַּעֲלַת חָמֵשׁ. תַּלְמוּד לוֹמַר (דברים כב יב) ״אֲשֶׁר תְּכַסֶּה בָּהּ״ אֲפִלּוּ בַּעֲלַת חָמֵשׁ אוֹ יוֹתֵר עַל זֶה. וְלָמָּה אֲנִי מְחַיֵּב בַּעֲלַת חָמֵשׁ וּפוֹטֵר בַּעֲלַת שָׁלֹשׁ וּשְׁתֵּיהֶן אֵינָן בַּעֲלֵי אַרְבַּע כְּנָפוֹת. מִפְּנֵי שֶׁיֵּשׁ בִּכְלַל הֶחָמֵשׁ אַרְבַּע. לְפִיכָךְ כְּשֶׁהוּא עוֹשֶׂה צִיצִית לְבַעֲלַת חָמֵשׁ אוֹ שֵׁשׁ אֵינוֹ עוֹשֶׂה אֶלָּא לְאַרְבַּע כְּנָפַיִם הַמְרֻחָקוֹת זוֹ מִזּוֹ מֵאוֹתָן הֶחָמֵשׁ אוֹ הַשֵּׁשׁ בִּלְבַד. שֶׁנֶּאֱמַר עַל אַרְבַּע כַּנְפוֹת כְּסוּתְךָ:
"On the four corners of thy vesture" (Deuteronomy 22:12). This means that a garment requires fringes when it has four corners but not when it has three. But cannot the text also mean that the garment must have four fringes but not five? To guard against this inference, the text concludes, "wherewith thou coverest thyself", i.e., even if it has five corners or more. Why however should a garment with five corners be included in the obligation and one with three corners be exempted, seeing that neither has four corners? The answer is that the number five includes the number four. Accordingly, when fringes are inserted in a garment with five or six corners, they are to be inserted in those four of the five or six corners, that are furthest from each other, for it is said, "On the four corners of thy vesture."
More explicitly, the Rosh (Laws of Tzitzith 3:1) (cited by the Kesef Mishna) explaining a Sifrei, as well as Menachoth 37b, rules that any garment with more than four corners, including an eight cornered garment, only requires tzitzith on the outermost four corners:
והא דתניא בספרי בפרש' ועשו להם ציצית על כנפי בגדיהם שומע אני אף בעלי ג' ובעלי ה' ובעלי ו' ובעלי ז' ובעלי ח' במשמע ת"ל ארבע כנפות יצאו בעלי ג' ובעלי ה' ובעלי ו' ובעלי ז' ובעלי ח'. נ"ל דהכי פירושו אי לא כתיב אלא על כנפי בגדיהם ה"א דכל (ס"א שבכל) כנפים שיש לבגד אמרה תורה לעשות ציצית הן מעט הן הרבה ת"ל על ד' כנפות ונתמעטו מעט והרבה. ובעלי ג' פסול אף אם הטיל ארבע (ס"א והרבה ונתמעטו בעלי ג' שהוא פסול אף אם הטיל בו בד' ציצית) דעל ארבע בעיא וליכא. ונתמעטו בעלת ה' ויותר שאין להטיל בכל הכנפים אלא בד' מהם:
That which was taught in the Sifrei regarding the passage "and they shall make for themselves fringes on the corners of their garments": "I hear even [garments] of three, five, six, seven, or eight [corners] are implied..." [implying that they are actually not required to have fringes]. It appears to me that this is the explanation [of this passage of Sifrei]: If it was only written "...on the corners of their garments", I would have thought that all the corners of the garment are required by the Torah to have fringes, whether there are few or many. Thus, [we derive from the verse:] "on the four corners" and many and few are excluded. And three-cornered [garments] are invalid [for the commandment] even if he put [on them fringes] for [they] need to be placed on four corners which they do not have. And [a garment] with five or more corners are excluded [from having the fringes on all their corners] for [the fringes] are not to be put on all the corners, rather only on four of them.
Likewise, the Shulchan Arukh rules (without caveat or comment of the Ramo):
טלית שאין לה ד' כנפו' פטורה יש לה יותר מארבע חייבת ועושה לה ארבע ציציות בארבע כנפו' המרוחקות זו מזו יותר:
A tallit with less than four corners is exempt [from the requirement of tzitzit]. One with more than four corners requires tzitzit, and they should be put on the four corners that are the furthest from each other.
What happens when wearing an octagon? Would a doubt over which four corners are "outermost" require stringing all 8? Or (as I suspect) that would be bal tosif (do not add [to the mitzvos]) and you just pick 4 that are roughly evenly scattered? Oct 13, 2021 at 14:15
@MichaBerger Generally, when we are strict out of uncertainty, it's not an issue of bal tosif - e.g. yontev sheini.– LoewianOct 13, 2021 at 16:42
@Loewian I think that's way too general. The Rosh is quite concerned about bal tosif concerning the tefillin of Rabbeinu Tam, and so too the poskim discussing putting on tefillin on Chol Hamoed. See also the Beis Yosef when he discussed the idea of putting tzitzis through double holes, both ends coming out on the same side of the garment; he really doesn't want you putting one set of each type at each corner.– MichoelROct 15, 2021 at 2:26
@MichaBerger R' Micha, the Aruch Hashulchan says somewhere that the idea of "outermost" corners is based on the "four corners of the earth". With eight corners you probably pick every other one, whichever? I'm wondering what you'd do with five corners, unevenly spaced - how do you define "outermost"?– MichoelROct 15, 2021 at 2:29
@MichoelR, I think the Arukh haShulchan Yomi Facebook group had a discussion of it when AhS Yomi aishdas.org/ahs-yomi was on the topic. In any case, you should maximize total distance between tzitziyos. (OC 10:2 sefaria.org/Arukh_HaShulchan%2C_Orach_Chaim.10.2 ). He mentions bal tosif to put on more than 4. Which is why I asked what to do when there is more than one way to choose corners such that you maximized the distance between those with tassels. The number one solution is a tie. Oct 15, 2021 at 15:23