Funnily enough, diamonds are one of the few gems which can be cut using Kyven's techniques.
The technique is called cleaving, and is used to breack a stone along crystaline cleavage planes (not necesarilly paralel to the crystal faces). The most common stones which show perfect cleavage are flourite (those octohedrons you see in most new-age shops are mostly cleaved), Calcite - Iceland Spar (those rhombs which show double refraction), and Topaz (perpendicular to the main axis of the crystal)
The problem with cleaving, is that while the surfaces seem flat, there are usually annoying steps because the crystal cleaves along a plane, but at several layers. It is also almost impossible to polish flat along a cleavage plane due to these weaknesses.
Cleaving of diamonds was used in the medieval period to shape the stone into a more perfect octohedron, and was later used to braeck large mis-shapen stones into smaller ones more suitable for cutting. It is said the when Joseph Asscher cleaved the Cullinan, he fainted because of the stress.
http://www.diamonds-are-forever.org.uk/ ... iamond.htm
Fancy cuts like the scisors cut mentioned in one of the early chapters are impossible by cleaving on natural stones. (I havent said anything because the "crystals" in the story are clearly unnatural stones.)
Modern cutting techniques involve grinding the stone with different grades of grit (usualy synthetic diamond) on a flat wheel, with a stepped stone holder so that the different facets are regular.
I'm no expert cutter, but I have cut several stones, including sapphires, garnets, rock crystal and aquamarine.