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Crystals can be classified in three ways: lattice systems, crystal systems and crystal families. The various classifications are often confused: in particular the trigonal crystal system is often confused with the rhombohedral lattice system, and the term "crystal system" is sometimes used to mean "lattice system" or "crystal family".
In crystallography, the orthorhombic crystal system is one of the 7 crystal systems. Orthorhombic lattices result from stretching a cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular prism with a rectangular base ( a by b ) and height ( c ), such that a , b , and c are distinct.
It can be used to define the rhombohedral lattice system, a honeycomb with rhombohedral cells. A rhombohedron has two opposite apices at which all face angles are equal; a prolate rhombohedron has this common angle acute, and an oblate rhombohedron has an obtuse angle at these vertices.
These threefold axes lie along the body diagonals of the cube. The other six lattice systems, are hexagonal, tetragonal, rhombohedral (often confused with the trigonal crystal system), orthorhombic, monoclinic and triclinic.
However, the rhombohedral axes are often shown (for the rhombohedral lattice) in textbooks because this cell reveals the 3 m symmetry of the crystal lattice. The rhombohedral unit cell for the hexagonal Bravais lattice is the D-centered [ 1 ] cell, consisting of two additional lattice points which occupy one body diagonal of the unit cell with ...
R rhombohedral; A reflection plane m within the point groups can be replaced by a glide plane, labeled as a, b, or c depending on which axis the glide is along. There is also the n glide, which is a glide along the half of a diagonal of a face, and the d glide, which is along a quarter of either a face or space diagonal of the unit cell.
Numerous examples are known with cubic, tetragonal, rhombohedral, and orthorhombic symmetries. Monoclinic and triclinic examples are certain to exist, but have proven hard to parametrise. [1] TPMS are of relevance in natural science. TPMS have been observed as biological membranes, [2] as block copolymers, [3] equipotential surfaces in crystals ...
Likewise, in 3 dimensions, there are 14 Bravais lattices: 1 general "wastebasket" category (triclinic) and 13 more categories. These 14 lattice types are classified by their point groups into 7 lattice systems (triclinic, monoclinic, orthorhombic, tetragonal, cubic, rhombohedral, and hexagonal).