Bravais lattice

A Bravais lattice is an infinite periodic array of points generated by integer combinations of primitive translation vectors. Every lattice point has an identical environment.

Lattice vector: A vector that translates a lattice point to another lattice point. Integer combinations of these vectors generate every point in the lattice.
Translational symmetry: Symmetry under shifting a structure by a fixed displacement. Lattice translations reproduce the array without changing its arrangement.
Cubic crystal system: A crystal system with equal unit-cell edges and three right angles. Its primitive, body-centered, and face-centered forms are distinct Bravais lattices.
Crystal structure: A periodic arrangement of atoms, ions, or molecules described by a lattice and a basis. Unlike a Bravais lattice alone, it specifies the objects repeated at each point.
Primitive unit cell: A smallest-volume cell whose translations reproduce a lattice and contain one lattice point on average. Its three edge vectors can serve as primitive translation vectors.
Wigner–Seitz cell: The region closer to one lattice point than to any other. It gives a symmetry-centered choice of primitive cell for any Bravais lattice.
Face-centered cubic: A cubic lattice with points at the cube corners and face centers. It is one of the fourteen three-dimensional Bravais lattice types.
Non-Bravais lattice: A periodic arrangement with multiple inequivalent sites in a chosen repeating description. Such arrays require multiple site types rather than one equivalent point per lattice position.
Lattice point: A point in a periodic array whose surroundings are identical to those of every other point. The array consists of equivalent points, not atoms or other objects by definition.
Miller indices: Integer labels that specify directions and planes relative to crystallographic axes. They describe lattice directions and plane families using a chosen unit cell.

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