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32 relations: Bravais lattice, Brillouin zone, Crystal, Crystal structure, Crystallography, Cube, Cubic crystal system, Cuboid, Fundamental domain, Geometry, Hexagonal crystal family, Lattice (group), Mineralogy, Monoclinic crystal system, Orthorhombic crystal system, Parallelepiped, Parallelogram, Position and momentum space, Prism (geometry), Reciprocal lattice, Rectangle, Rhombus, Solid-state physics, Space group, Square, Tetragonal crystal system, Translational symmetry, Triclinic crystal system, Trigonal trapezohedron, Voronoi diagram, Wallpaper group, Wigner–Seitz cell.
Bravais lattice
In geometry and crystallography, a Bravais lattice, named after, is an infinite array of discrete points in three dimensional space generated by a set of discrete translation operations described by: where ni are any integers and ai are known as the primitive vectors which lie in different directions and span the lattice.
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Brillouin zone
In mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell in reciprocal space.
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Crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions.
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Crystal structure
In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material.
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Crystallography
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids (see crystal structure).
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Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
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Cubic crystal system
In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube.
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Cuboid
In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube.
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Fundamental domain
Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action.
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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Hexagonal crystal family
In crystallography, the hexagonal crystal family is one of the 6 crystal families, which includes 2 crystal systems (hexagonal and trigonal) and 2 lattice systems (hexagonal and rhombohedral).
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Lattice (group)
In geometry and group theory, a lattice in \mathbbR^n is a subgroup of the additive group \mathbb^n which is isomorphic to the additive group \mathbbZ^n, and which spans the real vector space \mathbb^n.
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Mineralogy
Mineralogy is a subject of geology specializing in the scientific study of chemistry, crystal structure, and physical (including optical) properties of minerals and mineralized artifacts.
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Monoclinic crystal system
In crystallography, the monoclinic crystal system is one of the 7 crystal systems.
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Orthorhombic crystal system
In crystallography, the orthorhombic crystal system is one of the 7 crystal systems.
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Parallelepiped
In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning).
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Parallelogram
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides.
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Position and momentum space
In physics and geometry, there are two closely related vector spaces, usually three-dimensional but in general could be any finite number of dimensions.
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Prism (geometry)
In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases.
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Reciprocal lattice
In physics, the reciprocal lattice represents the Fourier transform of another lattice (usually a Bravais lattice).
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Rectangle
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.
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Rhombus
In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length.
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Solid-state physics
Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy.
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Space group
In mathematics, physics and chemistry, a space group is the symmetry group of a configuration in space, usually in three dimensions.
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Square
In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.
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Tetragonal crystal system
In crystallography, the tetragonal crystal system is one of the 7 crystal systems.
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Translational symmetry
In geometry, a translation "slides" a thing by a: Ta(p).
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Triclinic crystal system
Triclinic (a ≠ b ≠ c and α ≠ β ≠ γ) In crystallography, the triclinic (or anorthic) crystal system is one of the 7 crystal systems.
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Trigonal trapezohedron
In geometry, a trigonal trapezohedron or trigonal deltohedron is a three-dimensional figure formed by six congruent rhombi.
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Voronoi diagram
In mathematics, a Voronoi diagram is a partitioning of a plane into regions based on distance to points in a specific subset of the plane.
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Wallpaper group
A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern.
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Wigner–Seitz cell
The Wigner–Seitz cell, named after Eugene Wigner and Frederick Seitz, is a type of Voronoi cell used in the study of crystalline material in solid-state physics.
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References
[1] https://en.wikipedia.org/wiki/Primitive_cell
