Hexagonal crystal family in the context of "Ice crystals"

In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices (an infinite array of discrete points). Space groups (symmetry groups of a configuration in space) are classified into crystal systems according to their point groups, and into lattice systems according to their Bravais lattices. Crystal systems that have space groups assigned to a common lattice system are combined into a crystal family.

The seven crystal systems are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. Informally, two crystals are in the same crystal system if they have similar symmetries (though there are many exceptions).

Cleavage, in mineralogy and materials science, is the tendency of crystalline materials to split along definite crystallographic structural planes. These planes of relative weakness are a result of the regular locations of atoms and ions in the crystal, which create smooth repeating surfaces that are visible both in the microscope and to the naked eye. If bonds in certain directions are weaker than others, the crystal will tend to split along the weakly bonded planes. These flat breaks are termed "cleavage". The classic example of cleavage is mica, which cleaves in a single direction along the basal pinacoid, making the layers seem like pages in a book. In fact, mineralogists often refer to "books of mica".

Diamond and graphite provide examples of cleavage. Each is composed solely of a single element, carbon. In diamond, each carbon atom is bonded to four others in a tetrahedral pattern with short covalent bonds. The planes of weakness (cleavage planes) in a diamond are in four directions, following the faces of the octahedron. In graphite, carbon atoms are contained in layers in a hexagonal pattern where the covalent bonds are shorter (and thus even stronger) than those of diamond. However, each layer is connected to the other with a longer and much weaker van der Waals bond. This gives graphite a single direction of cleavage, parallel to the basal pinacoid. So weak is this bond that it is broken with little force, giving graphite a slippery feel as layers shear apart. As a result, graphite makes an excellent dry lubricant.

Hematite (/ˈhiːməˌtaɪt, ˈhɛmə-/), also spelled as haematite, is a common iron oxide compound with the formula Fe₂O₃ and is widely found in rocks and soils. Hematite crystals belong to the rhombohedral lattice system which is designated the alpha polymorph of Fe
₂O
₃. It has the same crystal structure as corundum (Al
₂O
₃) and ilmenite (FeTiO
₃). With this crystal structure geometry it forms a complete solid solution at temperatures above 950 °C (1,740 °F).

Hematite occurs naturally in black to steel or silver-gray, brown to reddish-brown, or red colors. It is mined as an important ore mineral of iron. It is electrically conductive. Hematite varieties include kidney ore, martite (pseudomorphs after magnetite), iron rose and specularite (specular hematite). While these forms vary, they all have a rust-red streak. Hematite is not only harder than pure iron, but also much more brittle. The term kidney ore may be broadly used to describe botryoidal, mammillary, or reniform hematite. Maghemite is a polymorph of hematite (γ-Fe
₂O
₃) with the same chemical formula, but with a spinel structure like magnetite.