In reality, the only fact which is known with absolute certainty is the color of each stone. Although absent from the Biblical passages, this is recorded by the Midrash (Bamidbar Rabbah 2:7) where it

Thus even if some doubt exists with regard to the scientific classification of the gems themselves, we can still be certain as to their appearance based on the Midrashic description of their colors (again, arbitrarily using the 12 "most representative" names we have chosen for the purpose of listing them):

Ruby - Reuben - Red

Jade - Shimon - Green

Agate - Levi - Red, White, and Black Striped

Carbuncle - Judah - Bluish-Green

Lapis-Lazuli - Issachar - Blue

Quartz Crystal - Zebulun - Clear

Turquoise - Dan - Blue

Amethyst - Naftali - Purple

Agate - Gad - Grey

Aquamarine - Asher - Blue-Green

Onyx - Joseph - Black

Opal - Benjamin - A Stone Possessing All the Colors