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28:21 The stones shall contain the names of the twelve sons of Israel, one for each of the twelve [stones]. Each one's name shall be engraved as on a signet ring, to represent the twelve tribes.
Veha'avanim tihyeyna al-shemot beney-Yisra'el shteym esreh al-shemotam pituchey chotam ish al-shmo tihyeyna lishney asar shavet.


The stones shall contain...
  See note on Exodus 28:9. Some say that the names were simply in order of birth (Targum Yonathan; Midrash HaGadol, except that Issachar and Naphtali are transposed). The order is then (actually, it is reversed here, since Hebrew reads from right to left):

Reuben Simeon Levi
Judah Dan Naphtali
Gad Asher Issachar
Zebulun Joseph Benjamin

Others say that Jacob's sons were divided according to their mothers, with Leah's sons first, and Rachel's last (Shemoth Rabbah 38:10; Targum on Song of Songs 5:14;; Bachya; Chizzkuni; Tur). This is favored because leshem then comes out as Dan's stone (Baaley Tosafoth on Exodus 28:10; Rashi on Judges (18:29). The order is then:

Reuben Simeon Levi
Judah Issachar Zebulun
Dan Naphtali Gad
Asher Joseph Benjamin

According to some authorities, the names were ordered downward in columns rather than across in the rows (Minchath Chinukh 99).

The Midrash that discusses the colors of the stones (BeMidbar Rabbah 2:7) also has the same order, except that Gad and Naphtali are transposed (cf. Rashash ad loc.). This is the opinion used earlier.

Finally, there is an opinion that the tribes were in the same order as they camped in the desert (Numbers 2; Tzioni, BeMidbar; Otzar HaGeonim, Yoma 70; Targum Yonathan, Numbers 2:3; Zohar 2:230a; Siddur Rav Saadia Gaon, p 271; Abarbanel):

Judah Issachar Zebulun
Reuben Simeon Gad
Ephraim Manasseh Benjamin
Dan Asher Naphtali

If alternate rows are transposed, the order becomes very much like that of the earlier opinions, and Dan's stone remains the leshem (cf. Peliah p. 32a).

Reuben Simeon Gad
Judah Issachar Zebulun
Dan Asher Naphtali
Ephraim Manasseh Benjamin

In order for the breastplate to contain all the letters of the Hebrew alphabet, the names of the Patriarchs, Abraham, Isaac and Jacob were added, as well as the words shiv'tey Yeshurun, or 'tribes of Jeshurun' (Yoma 73b). Other sources give these last words as Shiv'tey Yah (Yad, K'ley HaMikdash 10:11; cf. Psalms 122:4), or Shiv'tey Yisrael (Yerushalmi, Yoma 1:3).

Some say that 'Abraham Isaac Jacob' were written on the first stone, and the other words on the last (Shemoth Rabbah 38:11; Yad, K'ley HaMikdash 9:7). Others maintain that they were divided among the stones so that there were six letters on each stone (Chizzkuni; Bachya). There were thus a total of 72 letters on the breastplate (Ibid.; Raziel HaMalakh p. 44).

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