Malbim: The stones on the Choshen were for Reuven, Shimon and Levi (the first row), Yehudah, Yisachar and Zevulun (second), Dan, Naftoli and Gad (third), Asher, Yosef and Binyamin (fourth). The gates are similar, but one tribe in each direction is switched to the opposite side. The north had the tribes of the first row, just Shimon was switched to the south. The south had the tribes of the second row, just Yehudah was switched to the north. The west had the tribes of the third row, just Gad was switched to the east. The east had the tribes of the fourth row, just Asher was switched to the west. There is a reason for this; it is not proper to elaborate here.