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Amethyst is a variety of quartz. It has a composition [chemical make-up] of SiO2 [silicon dioxide], as all varieties of quartz do. Pure Quartz with no inclusions or pigmentation [coloring] is called rock crystal. But amethyst is principally colored by traces of iron.
Amethyst belongs to the geological group named silicates-tectosilicates and has a trigonal or hexagonal crystal system. The color of amethyst is purple, and it bears a hardness of 7 on the moh's scale of hardness.

When streaked, amethyst appears white, and it bears a conchoidal fracture. Amethyst is 2.7 times heavier than water [has a specific gravity of 2.7] and can be turned into citrine with heat treatment.

So in summary, the composition, geological group, hardness, streak and specific gravity is the same as all quartz are. After all, amethyst is a variety of Quartz.

Quartz is the second most abundant mineral in the Earth's continental crust, after feldspar. It is made up of a continuous framework of SiO4 silicon-oxygen tetrahedra, with each oxygen being shared between two tetrahedra, giving an overall formula SiO2.

Amethyst is a violet variety of quartz often used in jewelry. The name comes from the Ancient Greek a- ("not") and methustos ("intoxicated"), a reference to the belief that the stone protected its owner from drunkenness; the ancient Greeks and Romans wore amethyst and made drinking vessels of it in the belief that it would prevent intoxication.

Source(s): wiki answers and Wikipedia