CELLS IN THE HEICHAL
(Mishnah 3): There were 38 cells (within the walls of the Heichal) -- 15 in the north, 15 in the south, and eight in the west.
The northern cells were in three rows of five, one row on top of another. The same applies to the southern cells;
The western cells were in three rows. The bottom two rows had three each, the top row had two.
There were three openings to each cell. One was to the (cell on the) right, one to the left, and one on top. (This refers to most cells. Some cells lacked some of these openings, e.g. cells on the extreme right and left or in the top row.)
The cell in the northeast corner (next to the north Pishpesh) had five openings -- to the right, on top, to the Mesibah (a winding pathway within the walls of the Heichal), to the Pishpesh, and to the Heichal. (This is like Chachamim (Mishnah 2), who say that the Heichal doors were opened from inside the Heichal.)
(Mishnah 4): (The interior width of) each bottom cell was five Amos; its ceiling was six Amos, which was the width of each intermediate cell. The ceiling of the latter was seven, which was the width of each top cell -- "ha'Yetzi'ah ha'Tachtonah Chamesh ba'Amah Rachbah veha'Tichonah Shesh ba'Amah Rachbah veha'Shelishis Sheva ba'Amah Rachbah."
(Mishnah 5): The Mesibah went up from the southeast corner to the northwest corner. Through it, one could go to the roofs of the cells;
One would ascend the Mesibah facing west and traverse the entire north, until reaching the west. He faces south and traverses the entire west, until reaching the south. He faces east and traverses the south, until reaching the opening to the Aliyah (second story), which was in the south.
At the opening to the Aliyah were two cedar poles (with rungs) to ascend to the roof of the Aliyah. (Rosh - young Kohanim would go up to check if repairs were needed.) The ends of beams demarcate between Kodesh and Kodesh ha'Kodashim. (The latter is directly above the lower Kodesh ha'Kodashim, which housed the Aron.)
There were openings in the roof of the Kodesh ha'Kodashim. When it was necessary to make repairs, they would lower workers in boxes (closed on three sides), lest the workers benefit from seeing more of the Kodesh ha'Kodashim than necessary.
MEASUREMENTS OF THE HEICHAL
(Mishnah 6): (All measurements are in Amos. The Ikar of the Heichal was the Kodesh, which housed the Menorah, Shulchan and inner Mizbe'ach, and the Kodesh ha'Kodashim. Sometimes "Heichal" includes its surrounding walls and cells, and sometimes the entire Ulam) The Heichal (including the Ulam) was 100 by 100, and 100 tall:
(Rosh - the visible part of) its base was six solid Amos; the (bottom story of the) Heichal was 40 tall, there was one Amah of Kiyor (lower, decorated ceiling beams), two of upper beams, one of ceiling planks, and one of cement. The Aliyah was 40. On top of it was one Amah of Kiyor, two of upper beams, one of ceiling planks, one of cement, a Ma'akah (protective railing) of three, and one Amah Kaleh Orev (spikes or a scarecrow to prevent ravens from perching on top);
R. Yehudah says, Kaleh Orev does not count towards the height. Rather, the Ma'akah was four Amos.
(Mishnah 7): The Heichal was 100 from east to west. The wall of the Ulam was five Amos, the Ulam was 11, the wall of the Heichal was six, the interior was 40, there was one Amah Traksin (a wall dividing between Kodesh and Kodesh ha'Kodashim in Bayis Rishon. In Bayis Sheni there were two curtains with an Amah between them), the Kodesh ha'Kodashim was 20, the wall of the Heichal was six, the cell (in back of it) was six, and the wall of the cell was five.
The Heichal (without the Ulam) was 70 from north to south. The wall of the Mesibah was five, the Mesibah was three, the wall of the cell was five, the cell was six, the wall of the Heichal was six, the interior was 20, the wall of the Heichal was six, the cell was six, the wall of the cell was five, Beis Horedes ha'Mayim (a gap between the wall of the cell and the south wall of the Heichal, water from the roof came through there); and the south wall of the Heichal was five;
The Ulam extended another 15 Amos to the north and 15 to the south. It was called Beis ha'Chalifos. Knives were stored there.
The Heichal is called Ari'el, for it is wide in front (100) and narrow in back (70), like a lion -- "Hoi Ari'el Ari'el Kiryas Chanah David." (The Rambam explains many of these Mishnayos differently. He says that the entire Heichal was (about) 100 wide. The walls were slanted; the back was slightly narrower than the front.)
LISHKOS IN THE AZARAH
(Mishnah 1): The entire Azarah was 187 long and 135 wide.
It was 187 from east to west. Ezras Yisrael and Ezras Kohanim were each 11, the Mizbe'ach was 32, it was another 22 until the Ulam (the steps occupied most or all of this space), the Heichal was 100, and there were 11 Amos in back of Kodesh ha'Kodashim.
(Mishnah 2): It was 135 from north to south. The ramp and Mizbe'ach together were 62 (even though each was 32, the ramp overlaps the Amah of the Sovev on the south, and the Amah (allotted) for the southern Yesod), there were eight Amos from the Mizbe'ach until the rings, the rings occupied 24, from the rings to the tables was four, from the tables to the pillars was four, and from the pillars to the wall of the Azarah was eight. The remainder (25) was split (evenly) between the extent of the pillars and the space from the south wall to the ramp. (Many ask how the tables could be four Amos from the pillars. In Tamid (30b), it says that the tables were between the pillars! The Rosh asks that slaughtered animals were flayed on the tables while hanging on hooks fixed in the pillars. Small animals are not four Amos long! Rosh concludes that our Mishnah discusses different tables. Rashash suggests that four Amos 'from the tables to the pillars' includes the area occupied by the tables, or that the tables could be unfolded or moved. Rashi (Yoma 16b) says that the tables occupied four Amos (the Tana did not need to teach this, it is explicit in Yechezkel), so only 21 Amos remained.)
(Mishnah 3): There were six Lishkos in the Azarah, three in the north and three in the south. In the north were:
Lishkas ha'Melach, where salt for Korbanos was kept;
Lishkas ha'Parvah, where they salted hides of Kodshim. On top of it was a Mikveh where the Kohen Gadol immersed on Yom Kipur;
Lishkas ha'Madichim, where they would rinse innards of Korbanos. From there, the Mesibah ascends to the roof of Beis ha'Parvah.
(Mishnah 4): The (three) Lishkos in the south were Lishkas ha'Etz, Lishkas ha'Golah and Lishkas ha'Gazis.
R. Eliezer ben Yakov: I forgot what Lishkas ha'Etz was used for.
Aba Sha'ul: This is (Lishkas Parhedrin,) where the Kohen Gadol would stay (the week before Yom Kipur).
It was in back of the other two. (Tosfos Yom Tov - Lishkas ha'Gazis was to its east, and Lishkas ha'Golah was to its west.) All three had a common roof.
In Lishkas ha'Golah was a wheel to draw water (from a pit) for the entire Azarah (for the Kiyor, or for drinking).
The Sanhedrin Gedolah sat in (the Chol part of) Lishkas ha'Gazis. They would judge the Kashrus of Kohanim (who came to serve for the first time. Tosfos Yom Tov - they judged also Leviyim. The Mishnah discusses Kohanim, since that was primary, or because only Kohanim would celebrate being found Kosher):
If a Kohen was found to be Pasul, he would wear black clothes and leave;
If he was found to be Kosher, he would wear white (Tiferes Yisrael - Bigdei Kehunah; Rosh - this was to show his Simchah) and serve with the other Kohanim. (Surely, his first Avodah is to bring his Minchas Chinuch);
He would make a Yom Tov, and praise Hash-m that no Pesul was found in the seed of Aharon, and for choosing (Kohanim Gedolim from) Aharon and his seed to serve Him in the Kodesh ha'Kodashim.