1. A Sukkah whose Sunlit Area Exceeds its Shaded Area, & Other Laws Governing S’chach, containing 10 Seifim: A sukkah who's sunlit area is equal to its shaded area from above is invalid according to the idea that the sunlight diffuses as it gets more distant and is greater than the shaded area. However, if the sunlit area and shaded area are equal from below, it is valid.
2. A sukkah is valid if the majority of the s’chach casts a shadow whose area is two small measures greater than the sunlit area and hence the empty space in the s’chach is [considered as] very little, while [under] a smaller part of the s’chach, the sunlit area exceeds the shaded part by a small measure. RAMA: There are those who are stringent if the sukkah is large and there is a space that is 7 x 7 (tefachim) where the sunlight is the majority, even though when combined the entire sukkah has more shaded area (R"an).
3. As an initial and preferred option, the s’chach should be light so that large stars to be seen through it at night. [After the fact] even if [the s’chach] was very thick, [making it seem] like [the roof of] a house and not allowing the stars to be seen, it is valid.
4. If the s’chach is a very light covering with much empty space, but no one place has three handbreadths of empty space [the sukkah] is valid, [provided] the overall shaded part [of its floor] exceeds its sunlit area; i.e., there is more s’chach than open space.
5. If the s'chach is tangled and irregular i.e., parts of it were on a somewhat higher level and parts were on a somewhat lower level, it is valid. Provided that the vertical distance between the higher level and the lower level [of the s’chach] is less than three handbreadths. If the width of the upper one is a tefach or more, even though it is higher than three tefachim, we consider [the s’chach on] the higher level as if it had descended and was positioned in the empty space under it. RAMA: In other words, there is a tefach in the space of the bottom one such that one could bring down the top one and then it is valid, even if its sunlit area exceeds the shaded area, since when the sun is at its zenith, directly overhead, the shaded part [of the sukkah floor] does exceed its sunlit area, [the sukkah] should not be disqualified because of sunlight that comes in [at other times] from the side, at an angle.
6. Poles that come out from the back of the sukkah, for example when the canes of the s’chach project beyond the fourth side of the sukkah, if the canes [covering this addition] extend over the minimum dimensions of a sukkah, and its shade exceeds its sunlit area, the three walls are valid even though the middle wall wasn't made for it but rather for the essence of the sukkah, which is inside of it. [Note: For [even if the latter were to be the builder’s intent,] we are not concerned with his intent (for there is no requirement that a sukkah be built with the intent [that it be used for a mitzvah]. Thus it is as if he did not reveal his intent at all. [Rather,] the entire length of the s’chach is rendered valid by the third, short wall, even if it does not extend the entire length of the s’chach as does the opposite wall]
7. A similar [law applies] if the canes of the s’chach project beyond the fourth side of the sukkah, which is open and not enclosed by a wall, and one of the [parallel] walls extends outward with those canes. If the canes [covering this addition] extend over the minimum dimensions of a sukkah, this [additional] area is also considered as part of the sukkah and one may sit there even though it has only one wall. [These laws apply] even [when it is possible to say that] the owner of the sukkah revealed his intent to construct the entire sukkah with long walls, flanking the full length of the s’chach.
8. A person covered [the top of the sukkah] with [metal] spits, which are invalid as s'chach, and they do have 4 tefachim win them, and 4 tefachim from them to any one place, and he left a space the width of a spit between each pair of spits, and filled those spaces with valid s’chach, it is invalid, because it is impossible for a person to be exact and fill all the empty space between the spits with valid s’chach without leaving any space whatever between [any] spit and the [adjoining] valid s’chach. Hence, such a sukkah is not valid unless one placed on it a little additional valid s’chach to overlap the invalid s’chach, for then, all the empty space between the spits will certainly be covered. [This is certainly true with a large sukkah. But regarding a small sukkah, one must have less than three tefachim between the spits] (Beis Yosef; Maharal m'Prague].
9. [The following applies to] a house roofed with boards that are not covered by a maazivah (i.e., a clay floor that [sometimes] overlays them), and [one desires] to make [the house] valid so that he can dwell under [the boards] for the sake of [the mitzvah of] a sukkah, or one grabs hold of one board of a set of two and places valid s'chach in its place - all of it is valid, even the boards which are wider than four tefachim. There is one (opinion) who says that the boards cannot be wider than four tefachim.
10. A sukkah without a roof, for example the tops of the walls were stuck together like a shed; or the top of the wall leans against the sukkah to create a wall - this is invalid. If it had a roof, even a small portion, or the leaning wall was raised to the wall from the earth for a small portion, this is valid. RAMA: There are those who say that this small space should not be empty space - only from the wall or the s'chach [Rosh in the name of the R"i; Rambam]. It must be 7 x 7 tefachim and higher than ten tefachim [Tur]. The walls, which are greater than ten, must also be made out of materials that can be used as s'chach [R"an]. If all of the walls are made of materials than can be used for s'chach one may sleep even under the walls [explanations of Rabbeinu Yerucham]