An Individual Gem Stone Attributed to Each of the Tribes
The Order of the Tribes on the Breastplate of the High Priest went from left to right i.e. in the same direction as the Hebrew Script.
The above illustration shows the Gem Stones of each of the Israelite Tribes. We agree with the order of the Tribes which is consistent with the Midrash BaMidbar Rabah though some authorities disagree with it. The colors are also similar to our understanding (in light of the Midrash) EXCEPT for the following: Levi was three colored stripes, red, black, and white. Judah had a light blue, rather than aquamarine). Asher had an aquamerine color that may somewhat have been more bluish. Benjamin had the colors of the rainbow. Other opinions exist.
It was commanded to make a breastplate for the High Priest with precious stones encased in it.
15 Fashion a breastpiece for making decisions,the work of skilled hands. Make it like the ephod: of gold, and of blue, purple and scarlet yarn, and of finely twisted linen. 16 It is to be square, a span long and a span wide, and folded double. 17 Then mount four rows of precious stones on it. The first row shall be carnelian, chrysolite and beryl; 18 the second row shall be turquoise, lapis lazuli and emerald; 19 the third row shall be jacinth, agate and amethyst; 20 the fourth row shall be topaz, onyx and jasper. Mount them in gold filigree settings. 21 There are to be twelve stones, one for each of the names of the sons of Israel, each engraved like a seal with the name of one of the twelve tribes.
The Shoham (onyx?) stone was associated with Joseph. Two of these stones were on the shoulders of the High priest in addition to one on the Breastplate. The names of the Twelve Tribes were written on these stones, six on each stone.
Rabbinical Hasidic Sources
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Characteristics of Joseph as explained by a Famous Rabbi
The word "Sefas Emes" (by Rabbi Yehuda Aryeh Leib Alter, 1847 - 1905), on Exodus 28:12 commented on the shoham stones on the shoulders. The Shoham (translated as "onyx") TWO SHOULDERPIECES stone on which the names of the twelve tribes were engraved was also the special stone of Joseph in the breastplate in which each tribe had its own stone.
Source of Illustration: http://www.templeinstitute.org/beged/priestly_garments-7.htm
"Sefas Emes" says on the significance of the Shoham stone being that of Joseph:
"The main point of the Memorial [Exodus 28:12 above] concerns Joseph and that is why on the Ephod [shoulder-piece of the High Priest] there was only the Shoham which is the stone of Joseph. By means of the stone of Joseph all the twelve stones are unified at their roots".
The names of the Tribes were also written on the stones on the Breastplate. The identity of the stones and also what particular stone belonged to which Tribe is disputed. We have adopted the most conventionally accepted Rabbinical opinions. For the order of the stones and of the Tribal Names we are relying on the Midrash Bamidbar Rabah.
The Stones and the Breastplate together were used to receive answers to questions concerning the whole community. This was known as the "Urim and Thumim."
URIM AND THUMMIM