- Lavud-How does one make a third wall using Lavud and Tzuras Pesach?[1]
If there are two walls in an L shape:[2] If one has two walls [each of at least seven Tefach long[3] and ten Tefach high] which are adjacent to each other in an L shape, then one is to place a plank which is slightly more than one Tefach wide[4] [more than 8.17 cm.[5], and is ten Tefach high] slightly within three Tefach [23.5 cm.[6]] from the ends of one of the walls. [Thus, through using the rule of Lavud it is considered that one has a plank of over four Tefachim, which is the majority of the length of a Kosher Sukkah.[7] According to some opinions, this requirement of a one Tefach wide pole slightly within three Tefachim of the wall is a Biblical obligation.[8]] One is then to establish a pole of any width opposite this plank, at the end of the wall[9] and make a Tzuras Pesach for the remaining space from this pole until the plank of more than one Tefach, by placing another plank over them. [This Tzuras Pesach then makes it as if there is a full third wall of seven Tefachim.[10] This Tzuras Pesach is only Rabbinically required to validate the third wall.[11] If the opposite wall extends more than seven Tefachim, then it is only necessary to establish the pole by the seven Tefach distance mark.[12]] The Tzuras Pesach is valid even if the plank is not resting directly on the pole and the more than Tefach long plank, so long as it hovers over them. It is disputed amongst the Poskim[13] as to whether the Sechach itself can serve as the Tzuras Pesach if it hovers over the pole and plank, and the main ruling is that one can be lenient. This above ability to create a wall using the rules of Lavud for a Tefach long plank and Tzuras Pesach is only valid for one of the three walls.[14] [It is however possible to use the rule of Lavud with a four Tefach long wall and then the rule of Lavud and Tzuras Pesach for another more than Tefach wall, as explained in C.]
If there are two parallel walls of seven Tefach:[15] If one has two walls [of at least seven Tefachim wide and ten Tefachim tall] which are parallel to each other, then [it is stricter than the above case of two L shaped walls[16] and] one is to place a plank which is slightly more than 4 Tefach wide [33 cm.[17] and ten Tefach tall] within three Tefach [23.5 cm.[18]] from the end of one of the walls.[19] [Hence using Lavud one has a total of 7 Tefach, which is the length necessary for a Kosher wall.] Nonetheless, even in this case, it is disputed in Poskim[20] as to whether one must in addition also establish a Tzuras Pesach as in the previous case, by placing a pole opposite the plank at the end of the wall and hovering a plank over it and the more than 4 Tefach plank. Practically, we rule that it is to have a Tzuras Pesach established.[21] This, however, only applies if the third wall is made using the rule of Lavud. If, however one contains a full seven Tefach wall for the third wall, then there is no need for a Tzuras Pesach to be made for the Sukkah to be Kosher.[22] [Likewise, if one contains two full walls of seven Tefachim and another two walls of more than four Tefachim, in the other directions, then there is no need to establish a Tzuras Pesach.[23] Likewise, if it is a very small Sukkah and the third four Tefach wall is within three Tefachim of both parallel walls, then it does not require a Tzuras Pesach.[24]]

[1] See Michaber 630:2-3; Piskeiy Teshuvos 630:1-7
[2] Michaber 630:2; Sukkah 6a
[3] See Halacha C for scenarios in which ity is valid even if only one of the walls contains seven Tefachim
[4] See M”B 630:8 as for why it must be more than one Tefach wide, when seemingly so long as it is more than half a Tefach wide it will suffice to take up majority of the seven Tefach length.
[5] 8.16 cm is the measurement of a Tefach Sachuk, as explained in the next footnote
[6] See Shiureiy Torah p. 249 that an Ama Dochakos is 47 cm. [as opposed to 48 for a regular Ama], and accordingly a Tefach Dochakos is 7.83 cm [i.e. 1/48 of a cm times 8, deducted from 8 centimeters] and by the Shiur Sukkah of 7×7 one should measure with the stringent approach of an Ama Sochakos, and the same would apply here Lechumra to measure the three Tefachim as Dochakos. See also M”B 633:2 and Shaar Hatziyon 633:2 that by Sukkah we follow the stringent approach in the dimensions, either Dochakos or Sochakos, and by the 7×7 dimension we follow Sochakos, and the same would apply here by the three Tefachim dimension; See also Midos Vishureiy Torah pp. 48-57 regarding Ama Sochakos and Dochakos; Piskeiy Teshuvos 633:1 writes that its 23.4 according to Grach Nah, when taking into account the Dochakos according to Chazon Ish, as he explains there in footnote 2
Other opinions-Chazon Ish: According to the Chazon Ish, the measurement is 28.26 cm following the 9.42 measurement of Tefach Dochakos. [See Piskeiy Teshuvos ibid]
[7] Taz 630:2; M”B 630:6; See M”B 630:8 as for why we need to have four Tefachim of a full wall, when seemingly so long as it is more than 3.5 Tefachim it will suffice to take up majority of the seven Tefach length.
[8] P”M 630 M”Z, brought in M”B 630:10; Biur Halacha 630:2 “Veyaaseh”. However, see Tosafos Sukkah 7b and P”M 630 A”A 7, who rule that it is only Rabbinically required, as Biblically, simply placing a Tefach pole adjacent to the wall suffices. [Biur Halacha ibid]
[9] Meaning, that if the wall is seven Tefachim long, then the pole is placed by the seven Tefach mark. [M”B 630:9 in name of M”A] However, some Poskim rule thatone is to place it one Tefach over in such a case, so the Tzuras Pesach always maintain a four Tefach distance. [M”B ibid in name of P”M in name of Hagahos Maimanis]
[10] Taz 630:2; M”B 630:6
[11] M”B 630:10; Biur Halacha 630:2 “Veyaaseh”
[12] Levushei Serud 630; P”M 631 A”A 4 in question on Levush; Shaar Hatziyon 630:2; Implication of ruling of Michbaer 631:7 regarding a Pesel that extends past the Sukkah
Other opinions: Some Poskim rule that one must establish the pole at the very end of the opposite wall, even if it is much longer than seven Tefachim. [Levush 630, brought and negated in Shaar Hatziyon ibid; Chazon Ish 75:8; Shevet Halevi 1:169]
[13] Rama ibid rule sthat it may while the M”A 630:2 rules that it may not. The M”B 630:13 concludes like the Rama
[14] Ateres Zekeinim 630; M”B 630:6 that the Halacha Lemoshe Misinai is that only one of the walls suffices to have a Tefach pole
[15] Michaber 630:3; Sukkah 6a; Piskeiy Teshuvos 630:5
[16] M”B 630:14
[17] Four Tefachim is 32.68 using the measurement of 8.16 cm per Tefach for a Tefach Sachuk, as explained in previous footnotes throughout this book
[18] See Shiureiy Torah p. 249 that an Ama Dochakos is 47 cm. [as opposed to 48 for a regular Ama], and accordingly a Tefach Dochakos is 7.83 cm [i.e. 1/48 of a cm times 8, deducted from 8 centimeters] and by the Shiur Sukkah of 7×7 one should measure with the stringent approach of an Ama Sochakos, and the same would apply here Lechumra to measure the three Tefachim as Dochakos. See also M”B 633:2 and Shaar Hatziyon 633:2 that by Sukkah we follow the stringent approach in the dimensions, either Dochakos or Sochakos, and by the 7×7 dimension we follow Sochakos, and the same would apply here by the three Tefachim dimension; See also Midos Vishureiy Torah pp. 48-57 regarding Ama Sochakos and Dochakos; Piskeiy Teshuvos 633:1 writes that its 23.4 according to Grach Nah, when taking into account the Dochakos according to Chazon Ish, as he explains there in footnote 2
Other opinions-Chazon Ish: According to the Chazon Ish, the measurement is 28.26 cm following the 9.42 measurement of Tefach Dochakos. [See Piskeiy Teshuvos ibid]
[19] See M”A 630:3 that perhaps this form of wall is only valid if it is within three Tefachim of the wall, and if not then it is invalid even with Tzuras Pesach, and that perhaps it must be within three Tefachim of both parallel walls. [P”M 630 A”A 4 in understanding of M”A ibid] However, see Machatzis Hashekel who claims there is an error in the M”A ibid and that it should read ten Amos, that only if the wall is a ten Amos distance from one of the walls is it invalid. Practically, the majority of Poskim negate this ruling of the M”A and conclude that it does not have to be within 3 Tefachim of both walls. [See M”B 630:15]
[20] Michaber ibid brings two opinions; first opinion says it needs a Tzuras Pesach, second opinion says it does not
[21] M”B 630:16 in name of Bach, Elya Raba
[22] Rama ibid
[23] Piskeiy Teshuvos ibid
[24] M”A 630:3 as explained in P”M 630 A”A 3 and Machatzis Hashekel ibid