Gemara

71b - Beraisa: Whenever it says 'Shesh' (regarding Bigdei Kehunah or curtains of the Mishkan) there were six threads (of each material in each strand of the Beged).

Each thread of the Choshen and Efod was of 28 strands.

72a - Question: What is the source of this?

Answer: "V'Asisa Choshen Mishpat...Zahav Techeiles v'Argamon v'Sola'as Shani v'Shesh Mashzar". There were six threads of each of the last four materials, and four of gold, making 28 in all.

Question: We should say that there were also six threads of gold!

Answer #1 (Rav Acha bar Yakov): "V'Kitzetz Pesilim" - Pesil alludes to two threads, so Pesilim alludes to four.

Answer #2 (Rav Ashi): We cannot have six threads, for we must fulfill "La'asos b'Soch ha'Techeiles uv'Soch ha'Argamon";

If there were two gold threads amidst each of the other four materials, there would be eight gold threads!

Suggestion: Perhaps there are two gold threads each amidst two of the other materials, and one gold thread each amidst the other two!

Rejection: "V'Asisa" teaches that we make all its components equally.

Rishonim

Question: Why is it clear that there cannot be eight gold threads in each strand?

Answer (Tosfos DH Na'avid): Four is the minimum. If we say more than four, there is no limit to what we will say.

Rambam (Hilchos Klei Makdish 9:5): To make the Choshen, each thread of gold is put with six threads of Techeiles, and all seven are folded like one. The same applies to the Argamon, Tola'as Shani and linen. In total there were 28 threads - La'asos b'Soch ha'Techeiles uv'Soch ha'Argamon".

Mishneh l'Melech (8:3, just before DH u'Shtei Kutanos): The Rambam holds that the threads each type of material were twined together. He argues with Rashi (Shmos 28:6), who says that in the end all of the threads are twined together.

Rashi (Shemos 28:30): 'Urim v'Tumim' refers to the Shem ha'Mefurash which was put between the folds of the Choshen; it caused the stones to be Me'ir (illuminate). In Bayis Sheni they had a Choshen, so the Kohen Gadol would not be Mechusar Begadim, but there was no Shem inside.

Tosfos (21b DH v'Urim): The Urim v'Tumim was in Bayis Sheni. If not, the Kohen Gadol would be Mechusar Begadim! However, it did not answer questions.

Rambam (Hilchos Beis ha'Bechirah 4:1): In Bayis Sheni they did not answer questions from the Urim v'Tumim with Ru'ach ha'Kodesh, so they did not ask.

Rebuttal (Ra'avad): Bayis Sheni was missing five things from Bayis Rishon, i.e. the Aron (with) Kapores and Keruvim, Esh (from Shomayim), Shechinah, Ru'ach ha'Kodesh, and the Urim v'Tumim (Yoma 21b). According to the Rambam, the Urim v'Tumim itself was there, only Ru'ach ha'Kodesh was missing. If so, there were only four things missing!

Answer (Kesef Mishneh): Perhaps the Rambam counts the Aron, Kapores and Keruvim as three, and Shechinah, Ru'ach ha'Kodesh, and the Urim v'Tumim as one. Alternatively he counts the Aron, Kapores and Keruvim as one, and Shechinah, Ru'ach ha'Kodesh, and the Urim v'Tumim as three; Ru'ach ha'Kodesh refers to prophecy.

Merkeves ha'Mishneh (Beis ha'Bechirah 4:1): The Rambam holds that Urim v'Tumim refers to the stones, which are Me'ir (illuminate). He counts Shechinah, Ru'ach ha'Kodesh and the Urim v'Tumim as one, because without Shechinah there is no Ru'ach ha'Kodesh and no Urim v'Tumim, i.e. the stones do not illuminate.

Rambam (ibid.): They had the Urim v'Tumim in Bayis Sheni so the Kohen Gadol would not be Mechusar Begadim.

Source (Kesef Mishneh Klei ha'Makdish 10:10): Kidushin 31a says that in the days of Bayis Sheni they sought stones for the Ephod.

Rebuttal (of Rambam - Ra'avad): The Urim v'Tumim is not considered one of the Bigdei Kehunah.

Kesef Mishneh: The Ra'avad understands that 'Urim v'Tumim' is the Shem ha'Mefurash. Here, the Rambam calls the Choshen 'Urim v'Tumim'.

Rebuttal (Even ha'Ezel): The Kesef Mishneh connotes that the Rambam agrees that they lacked Shem ha'Mefurash in Bayis Sheni. This is wrong. The Rambam (Hilchos Klei Makdish 10:10) says that the (only) reason they did not ask from the Urim v'Tumim was because there was not Ru'ach ha'Kodesh.

Rashbam (Shemos 28:16): The Choshen was like a pocket in which the Urim v'Tumim was put.

Da'as Zekenim mi'Ba'alei ha'Tosfos (28:16): There was an outer Choshen in which the stones were fixed, and an inner Choshen stuck to it to strengthen it.

Malbim (28:15): After it was folded, it was a square Zeres.

Rashi (25:7): The stones rest in and fill gold containers in the Choshen.

Rebuttal (Ramban 25:7): Each stone is on a setting in the Choshen. A three-pronged fork holds it in place.