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Mineral hardness is a diagnostic property that helps to identify and classify minerals. It's defined as the resistance of a mineral to being scratched. The Mohs scale of mineral hardness, created by Friedrich Mohs in 1812, is the standard scale against which the hardness of minerals is rated. It is a comparative, not an absolute scale, since it simply shows the order of hardness of minerals.

The scale assigns hardness values between 1 and 10 to minerals, with 1 being the softest (talc) and 10 being the hardest (diamond). Knowing the hardness of a mineral helps in understanding how it can be used and what it can be used upon. For instance, a higher number on the Mohs scale indicates that the mineral can scratch another mineral with a lower number. This property is essential when considering the use of minerals in various applications such as cutting, polishing, or grinding.

Calcite is a versatile mineral with numerous properties that make it useful for a wide range of applications. Chemically, it's composed of calcium carbonate (CaCO3) and is relatively soft, having a Mohs hardness of about 3. This softness means that calcite is easily scratched by substances with a higher hardness.

Calcite has many distinctive properties such as its high birefringence, which is used in optical devices, and its reaction with acids to produce carbon dioxide. However, because of its low hardness, calcite is not suitable for tasks that require a harder material, such as polishing harder minerals. In industrial uses, it's often found as a component in cement or as a pH stabilizer in soil.

A diamond's striking appearance is partly due to its facets, which are the flat surfaces cut onto the diamond to optimize its optical properties. These facets are carefully arranged in certain geometrical patterns to maximize the diamond's brilliance, fire, and scintillation.

When cutting a diamond, the goal is to form facets with precise angles and sizes that reflect and refract light to create the stone's sparkle. The process requires the use of materials much harder than the diamond, typically other diamonds or specially formulated diamond dust. Grinding a diamond with a substance softer than itself, such as calcite, would not alter the surface, thus highlighting the importance of the Mohs scale in gemstone faceting.