Topaz crystal surface and cleavage.
One of the characteristics of topaz is its perfect cleavage, which has nothing to do with the usual meaning we associate with this word, though it's a constant of corny geological jokes of the 'geologists make the bedrock' type. In minerals cleavage is a consequence of crystal structure and the regular arrangement of atoms in a lattice. In some crystals this arrangement has lines of weakness, where there are fewer bonds holding the atoms together and along which the crystal can easily break or be separated. Those of you who have played with a 'book' of mica crystals will have seen how it splits easily along parallel cleavage planes like pages in a book.
Cleavage is used to identify minerals, as its presence or absence will narrow the possibilities. it is described in terms of ease of splitting (called difficulty) and quality of split (eg perfect smooth faces like topaz or mica, or poor). If it is present, one then has to check if there is more than one smooth broken surface, and in which directions and angles they intersect to try and identify the crystal, obviously in conjunction with other properties like colour, lustre (how strongly it reflects light) and hardness. One may even have to try and reconstruct the crystal shape in a battered specimen.
Even diamond has cleavage, perfect in four directions, parallel to the faces of an octahedral crystal, a property used to break larger diamonds into smaller ones for faceting. A notch is cut in the crystal with another diamond, and a hammer and chisel used to split it. Needless to say this requires considerable planning and caution, a steady hand, and plenty of experience in squeezing value out of a rough stone, though nowadays CAD programs such as SARIN are used to supplement the experience of the cutters. When cleaving the largest diamond ever found, the Cullinan, the cleaver apparently fainted from nervous tension after striking a perfect blow that split it into the pieces that now grace the British crown jewels.
Topaz has one direction of perfect cleavage, which is parallel to the base and top of the crystal. Its crystals nearly always have flat bases, sometimes with steps, where pieces of the crystal have cleaved off. This photo shows some of these steps taken using a lighting technique called Nomarski differential interference contrast, that plays with wavelengths of light in order to reveal features that would otherwise be hard to see clearly. Calcite in contrast has three, resulting in the perfectly sculpted rhombs one can see in any mineral shop.
Needless to say, this property also makes it very difficult to facet such crystals, and they have to be orientated in such a way that placing it on the diamond impregnated polishing wheel will not lift off whole layers of the crystal along the cleavage planes, leaving you with a pile of dust and chips and no faceted gem.
Similar to cleavage is parting, but it doesn't occur along planes related to the arrangement of atoms in the crystal, but along twinning planes (where two or more crystals with different orientations have grown together) or stress lines imposed by its geological history (being squished in a mountain building episode for example). Crystals with several cleavage directions are invariably tricky, and faceters often get a high failure rate.
Image credit, magnification 30x: John Koivula