Synthetic diamond "nanocrystalline" and "microcrystalline" diamond, respectively. Synthetic diamond is the hardest known material, where hardness is defined as resistance to indentation. The hardness of synthetic diamond depends on its purity, crystalline perfection and orientation: hardness is higher for flawless, pure crystals oriented to the <nowiki>[</nowiki>111<nowiki>]</nowiki> direction (along the longest diagonal of the cubic diamond lattice). Nanocrystalline diamond produced through CVD diamond growth can have a hardness ranging from 30% to 75% of that of single crystal diamond, and the hardness can be controlled for specific applications. Some synthetic single-crystal diamonds and HPHT nanocrystalline diamonds (see hyperdiamond) are harder than any known
Mineral correspond to the symmetry operations that define the narrower point groups. They are summarized below; a, b, and c represent the axes, and α, β, γ represent the angle opposite the respective crystallographic axis (e.g. α is the angle opposite the a-axis, viz. the angle between the b and c axes): The hexagonal crystal family is also split into two crystal "systems" – the trigonal, which has a three-fold axis of symmetry, and the hexagonal, which has a six-fold axis of symmetry. Chemistry and crystal structure together define a mineral. With a restriction to 32 point groups, minerals of different