Diamonds are the hardest known mineral in the world, but they can be cut with another diamond. When cutting a diamond with a diamond, it is crucial that the mineral not be equally hard in every direction — if the diamond did not vary in hardness, it would be almost impossible to cut.

Diamonds are made of carbon arranged in a perfect crystal grid structure, in which every carbon atom is bound to four other carbon atoms. A diamond crystal belongs to the cubic crystal system, which is the simplest and most symmetrical crystal system. This means that a coordinate system with three equally long axes perpendicular to each other can be imposed into a diamond crystal. The simplest cubic crystal is a cube, and diamonds can actually grow like a cube, but it is more common for them to grow like octahedrons, which can be described as two four-sided pyramids attached together at the bottom. A diamond is hardest in directions parallel to the octahedron faces and softest parallel to the cube faces.

The tools used to cut diamonds are covered with diamond powder, all oriented differently and thus varying in hardness. In this way, some of the particles will always be harder than the face that is being cut, unless it is a face in the hardest direction. In this case, gem cutters must angle the cutting tool slightly in proportion to the hardest direction in order to cut the diamond.

The structure of a diamond means that it varies in hardness. It is softest parallel to the cube faces and hardest parallel to the octahedron faces. This difference is taken into account when the diamonds are cut.