How many different types of crystals are there and what are they?

Theres 7 types

triclinic

shapesmonoclinic

pyramidsorthorhombic

tetragonal

prismstrigonal

divisionhexagonal

cubic

I generally think in terms of crystal systems and lattice types. There are 7 crystal systems: triclinic - usually not symmetrical from one side to the other, which can lead to some fairly strange shapes. monoclinic - like skewed tetragonal crystals, often forming prisms and double pyramids.