Diamond crystallizes in the cubic system and its crystalline shapes are thus numerous, the principal ones are:
Octahedron

Dodecahedron

Cube

Rhombododecahedron. This is the crystal habit that is formed on a sub-atomic level.

Rough diamond classifications
 
After diamond was recovered, it will have to be sorted according to certain categories before being sold:   Diamonds for cleavage.
  Diamonds for sawing.
  Diamonds for cutting.
  Industrial diamonds.
 
Rough diamond can be sorted according to 3 distinct categories:   Gem quality.
 Industrial quality.
  Crushing-boart or boart.
 
Only 20 % of the world production of rough diamonds are intended for the jewellery (gem quality) and 80 % for the industrial uses. There would be more than 5,000 possible rough diamond classifications.

Gem quality diamond
 
It is this type of quality which will be used in the jewellery industry. It must be of good color and of good clarity, its shape is not very important because the diamond must be cut. This category of diamond requires a classification of the stones by subcategories.
See my other guide on diamond grading for specific details.

The stones: very beautiful stone of more than 1 carat. 
  The fancy colors stones are those with color that does not lies between the bluish white and the yellowish. The color of fancy colors diamonds is blue, green, pink, yellow, brown, etc...
  The closed stones: are monocrystals, beautiful shapes, good for sawing and polishing.
  The spotted stones: are monocrystals, beautiful shapes, these stones have inclusions but it is possible to make them disappear with the cutting.
  The naats: are deformations of crystallizations, they must be cleaved or bruted.
  The irregular stones: are octahedral or dodecahedral (irregular shapes), they are directly cut.
  The cleavable stones: they must be cleaved.
  The coated stones: the industry have named coated stones « speculation stones ». A gangue or a film covers them hiding the interior of the stone. They can remain opaque or let appear a beautiful stone.
  The frosted stones: are identical to coated, but the film is translucent.
  The milky stones: as its name indicates, this stone has a milky aspect.
  The blocks: of a particular shape, their crystallographic orientation is difficult to see.
  The plats: in fact generally macles are very often employed for the rose cut.
  The sands: they are very small stones (less than 0.10 carat), mostly used for the size 8/8
  The commons goods: they are of a very poor quality and they are the extreme product of the gem quality.
  The rejections stones: they are of very bad quality and therefore must be eliminated.