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2-dimensional lattice
The rectangular lattice and centered rectangular lattice (or rhombic lattice) constitute two of the five two-dimensional Bravais lattice types. The symmetry
Rectangular_lattice
Periodic set of points
Coordinate-wise addition or subtraction of two points in the lattice produces another lattice point. The lattice points are all separated by some minimum distance
Lattice_(group)
Classification of a two-dimensional repetitive pattern
square (square lattice, itself p4m). In the 5 cases of reflection or glide reflection, but not both, the cell is a rectangle (rectangular lattice, itself pmm)
Wallpaper_group
Geometry and crystallography point array
In geometry and crystallography, a Bravais lattice, named after Auguste Bravais (1850), is an infinite array of discrete points generated by a set of
Bravais_lattice
Type of three-dimensional crystal structural geometry
Orthorhombic lattices result from stretching a cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular prism with
Orthorhombic_crystal_system
Quadrilateral with sides of equal length
with exponent 1. One of the five 2D lattice types is the rhombic lattice, also called centered rectangular lattice. Rhombi can tile the 2D plane edge-to-edge
Rhombus
Classification of crystalline materials by their three-dimensional structural geometry
(oblique, rectangular, square, hexagonal), four crystal families (oblique, rectanguar, square, hexagonal), and four lattice systems (oblique, rectangular, square
Crystal_system
Lattice point group
Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square
Tetragonal_crystal_system
Cellular automaton traffic flow model
rectangular lattices with coprime dimensions, only periodic orbits exist. In 2008 periodic intermediate phases were also observed in square lattices.
Biham–Middleton–Levine traffic model
Biham–Middleton–Levine_traffic_model
Repeating unit formed by the vectors spanning the points of a lattice
two-dimensional Bravais lattices are represented using conventional primitive cells, as shown below. The centered rectangular lattice also has a primitive
Unit_cell
Allotrope of carbon
include a hexagonal lattice structure and a rectangular lattice structure. Out of the theorized structures the rectangular lattice of 6,6,12-graphyne may
Graphyne
Primitive cell in the reciprocal space lattice of crystals
In the same way the Bravais lattice is divided up into Wigner–Seitz cells in the real lattice, the reciprocal lattice is broken up into Brillouin zones
Brillouin_zone
Boundary set in the complex plane
+p_{d-1}z+p_{d}:=(z-\zeta _{1})(z-\zeta _{2})\cdots (z-\zeta _{d})} . Then for a rectangular lattice z m n = z 00 + m Δ x + i n Δ y ; m = 0 , … , M − 1 ; n = 0 , … ,
Newton_fractal
Type of plane partition
triangular lattice it is regular; in the case of a rectangular lattice the hexagons reduce to rectangles in rows and columns; a square lattice gives the
Voronoi_diagram
Sequence of end-to-end vectors across points of a lattice
. So the total number of lattice paths remains the same. Superimpose the NE lattice paths squared onto the same rectangular array, as seen in the figure
Lattice_path
Structure deriving strength from a double curvature
initially laying out the main lath members flat in a regular square or rectangular lattice, and subsequently deforming this into the desired doubly curved form
Gridshell
Superconducting transmon 9×6 lattice —N/a 53 effective (54 total) 2019 Google Willow Superconducting transmon rotated rectangular lattice (see spec sheet) 99.965%
List_of_quantum_processors
Type of geometry for connecting computer nodes
degree of four, the nodes are imagined laid out in a two-dimensional rectangular lattice of n rows and n columns, with each node connected to its four nearest
Torus_interconnect
Semigroup in which every element is idempotent
square). Bands were first studied and named by A. H. Clifford (1954). The lattice of varieties of bands was described independently in the early 1970s by
Band_(algebra)
Theorem about admissible crystal symmetries
specific lattice. For example, a 60° rotation will not work with a square lattice; nor will a 90° rotation work with a rectangular lattice. When the
Crystallographic restriction theorem
Crystallographic_restriction_theorem
Logic puzzle
puzzle developed by publisher Nikoli. Slitherlink is played on a rectangular lattice of dots. Some of the squares formed by the dots have numbers inside
Slitherlink
being the maximal lattice image of S {\displaystyle S} , thus making every skew lattice S {\displaystyle S} a lattice of rectangular subalgebras. This
Skew_lattice
Dense arrangement of congruent spheres in an infinite, regular arrangement
in a rectangular or triangular wooden frame, forming a three-sided or four-sided pyramid. Both arrangements produce a face-centered cubic lattice – with
Close-packing of equal spheres
Close-packing_of_equal_spheres
Tool for digital signal processing
the frequency regions in Figure can be critically sampled by the rectangular lattice spanned by D 1 {\displaystyle D_{1}} . So imagine the filter bank
Filter_bank
Tessellation of Euclidean space
points on the integer lattice. A rectilinear grid is a tessellation by rectangles or rectangular cuboids (also known as rectangular parallelepipeds) that
Regular_grid
Type of symmetry group
spaces of points in projective spaces, and transfer matrices in solvable lattice models. Formally, a frieze group is a class of infinite discrete symmetry
Frieze_group
Lattice formed by all integer partitions
In mathematics, Young's lattice is a lattice that is formed by all integer partitions. It is named after Alfred Young, who, in a series of papers On quantitative
Young's_lattice
Physical Process
differences may be a result of either anisotropy in the surface lattice (e.g. a rectangular lattice) or the presence of steps on a surface. One of the more dramatic
Surface_diffusion
Theorem in sampling theory
The sampling density to achieve this is equal to the area of the rectangular lattice cell of the spectrum replication. The corresponding area of the rectangle
Papoulis-Marks-Cheung Approach
Papoulis-Marks-Cheung_Approach
Fluid dynamics study of flow distribution in parallel channels
D.; Fan, Y.; Commenge, J.M.; Luo, L. (2011). "Uniform flows in rectangular lattice networks". Chemical Engineering Science. 66 (21): 5301–5312. Bibcode:2011ChEnS
Flow distribution in manifolds
Flow_distribution_in_manifolds
Method for capturing hyperspectral images
Alenin, and J. S. Tyo, "Focal plane filter array engineering I: rectangular lattices", Optics Express 25: 10 (2017). M. A. Bershady, "3D spectroscopic
Snapshot hyperspectral imaging
Snapshot_hyperspectral_imaging
rectangular lattice. Similarly periodic replication of the hexagonal region of support maps to sampling the continuous signal on a hexagonal lattice.
Hexagonal_sampling
One of the 7 crystal systems in crystallography
monoclinic Bravais lattices exist: the primitive monoclinic and the base-centered monoclinic. In the base-centered monoclinic lattice, the primitive cell
Monoclinic_crystal_system
Optical filter
Fourier optics): where for mathematical simplicity, we assume a rectangular lattice in which α only depends on m and β only depends on n. In the equations
Frequency_selective_surface
Model in Quantum Physics
mechanics, the particle in a one-dimensional lattice is a problem that occurs in the model of a periodic crystal lattice. The potential is caused by ions in the
Particle in a one-dimensional lattice
Particle_in_a_one-dimensional_lattice
Mathematical functions
\operatorname {cd} } with positive real elliptic modulus have an "upright" rectangular lattice aligned with real and imaginary axes. Alternately, the functions
Lemniscate_elliptic_functions
Numerical method used in computational fluid dynamics
The Vortex lattice method, (VLM), is a numerical method used in computational fluid dynamics, mainly in the early stages of aircraft design and in aerodynamic
Vortex_lattice_method
Geometric construct
viewing from the dual lattice, each frustrated edge must be "covered" by a 1x2 rectangle, such that the rectangles span the entire lattice and do not overlap
Domino_tiling
The lattice stool was the most popular type of stool in ancient Egypt. It is rectangular in form with a combination of features. These features would include:
Lattice_stool
Primitive cell of crystal lattices with Voronoi decomposition applied
cell for any given lattice. It is the locus of points in space that are closer to that lattice point than to any of the other lattice points. A Wigner–Seitz
Wigner–Seitz_cell
the frequency regions in Figure can be critically sampled by the rectangular lattice spanned by D 1 {\displaystyle D_{1}} . So imagine the filter bank
Multirate filter bank and multidimensional directional filter banks
Multirate_filter_bank_and_multidimensional_directional_filter_banks
Tree data structure that partitions a 2D area
interesting spatial information". The subdivided regions may be square or rectangular, or may have arbitrary shapes. Although similar subdivisions were used
Quadtree
Integer factorization algorithm
implementing the inmost loop, since listing the elements of a lattice within a rectangular region efficiently is itself a non-trivial problem, and efficiently
Lattice_sieving
Special mathematical function defined as sin(x)/x
function. The normalized sinc function is the Fourier transform of the rectangular function with no scaling. It is used in the concept of reconstructing
Sinc_function
Mathematical description in crystallography
{\displaystyle {\mathcal {F}}} [lattice] × F {\displaystyle \times {\mathcal {F}}} [basis] ∗ F {\displaystyle \ast {F}} [rectangular function]; that is, scattering
Structure_factor
Vector representing lattice distortion due to dislocations in a crystal
represents the magnitude and direction of the lattice distortion resulting from a dislocation in a crystal lattice. The vector's magnitude and direction is
Burgers_vector
to sample two-dimensional fields is to sample it at points on a rectangular lattice. However, this is not always the ideal choice in terms of the sampling
Multidimensional_sampling
Indian physicist and administrator
Sinha, Ravindra Kumar (2017). "SBS based slow-light generation in rectangular lattice graded-index photonic crystal fiber: Design and analysis". Optik
Ravindra Kumar Sinha (physicist)
Ravindra_Kumar_Sinha_(physicist)
Quasiregular space-filling tesselation
vertex arrangement represents an A3 lattice or D3 lattice. This lattice is known as the face-centered cubic lattice in crystallography and is also referred
Tetrahedral-octahedral honeycomb
Tetrahedral-octahedral_honeycomb
History of geometrical crystallography to 1895
discovery of the 7 crystal systems, the 32 crystal classes, the 14 Bravais lattices, and the 230 space groups. The study of the geometrical properties of crystals
Geometrical crystallography before X-rays
Geometrical_crystallography_before_X-rays
Invariance of operations under geometric translation
two given lattice points, equivalence of choices of a third point to generate a lattice shape is represented by the modular group, see lattice (group).
Translational_symmetry
English mathematician and statistician
M.J.R. Healy) Grundy, P. M. (1950), "The estimation of error in rectangular lattices", Biometrics, 6 (1): 25–33, doi:10.2307/3001421, JSTOR 3001421 "A
Patrick_Michael_Grundy
Relationship between elements of two sets
Cartesian product X × Y . {\displaystyle X\times Y.} Since a powerset is a lattice for set inclusion ( ⊆ {\displaystyle \subseteq } ), relations can be manipulated
Binary_relation
Property of objects which appear unchanged after a partial rotation
of a parallelogrammic, rectangular, and rhombic lattice. p3 (333): 3×3-fold; not the rotation group of any lattice (every lattice is upside-down the same
Rotational_symmetry
Equation in Fourier analysis
^{n})} (L1 for L1 space) and Λ {\displaystyle \Lambda } is a unimodular lattice in R n {\displaystyle \mathbb {R} ^{n}} . Then the periodization of f {\displaystyle
Poisson_summation_formula
Method of multivariate interpolation on a 3-dimensional regular grid
{\displaystyle (x,y,z)} within the local axial rectangular prism linearly, using function data on the lattice points. Trilinear interpolation is frequently
Trilinear_interpolation
Symmetry group of a configuration in space
3, called the Bravais lattice (so named after French physicist Auguste Bravais). There are 14 possible types of Bravais lattice. The quotient of the space
Space_group
Unmanned underwater vehicle (all variants); torpedo (M variants only)
as "High-Speed Autonomous Underwater Effects". Copperhead features a rectangular hull form, rather than the cylindrical hull shapes of the Mk54 and Mk48
Copperhead_(UUV)
Structure whose members are only in tension
The world's first steel membrane roof and lattice steel shell in the Shukhov Rotunda, Russia, 1895
Tensile_structure
Gauge field loop operator
construct links and plaquettes which are the fundamental parameters in lattice gauge theory. Wilson loops fall into the broader class of loop operators
Wilson_loop
Bridge in Moscow, Russia
lead engineer and financial promoter. The bridge consisted of two rectangular lattice trusses (a mixed truss and girder type), each 65.5 meters long, with
Bolshoy_Krasnokholmsky_Bridge
Quadrilateral with two pairs of parallel sides
equal, or angles are right, the symmetry of the lattice is higher. These represent the four Bravais lattices in 2 dimensions. An automedian triangle is one
Parallelogram
OpenLB is an object-oriented implementation of the lattice Boltzmann methods (LBM). It is the first implementation of a generic platform for LBM programming
OpenLB
Describes the range of energies of an electron within the solid
quantum mechanical wave functions for an electron in a large, periodic lattice of atoms or molecules. Band theory has been successfully used to explain
Electronic_band_structure
Matrix of binary truth values
structure, the Boolean algebra U forms a lattice ordered by inclusion; additionally it is a multiplicative lattice due to matrix multiplication. Every logical
Logical_matrix
Bridge whose load-bearing superstructure is composed of a truss
bridge to protect the structure. In 1820, a simple form of truss, Town's lattice truss, was patented, and had the advantage of requiring neither high labor
Truss_bridge
openings; all have moulded hood moulds. The doorway has pilasters and a rectangular latticed fanlight. II Great Fernhill Farmhouse 52°53′09″N 3°01′00″W / 52
Listed buildings in Whittington, Shropshire
Listed_buildings_in_Whittington,_Shropshire
Doughnut-shaped surface of revolution
coordinate. That is, the n-torus is Rn modulo the action of the integer lattice Zn (with the action being taken as vector addition). Equivalently, the
Torus
Computational model of cells and tissues
regions of fluid. The CPM consists of a rectangular Euclidean lattice, where each cell is a subset of lattice sites sharing the same cell ID (analogous
Cellular_Potts_model
Cellular automaton
{\displaystyle N\times M} rectangular grid (checkerboard) Γ ⊂ Z 2 {\displaystyle \Gamma \subset \mathbb {Z} ^{2}} of the standard square lattice Z 2 {\displaystyle
Abelian_sandpile_model
Opening to admit light, air, or objects
load-bearing, muntins when not. Lattice light is a compound window pane madeup of small pieces of glass held together in a lattice. Fixed window is a unit of
Window
Mechanical engineer and academic
lattice Boltzmann method. He also developed lattice-Boltzmann models fully consistent with Navier-Stokes equations, such as the use of 2D rectangular
Lian-Ping_Wang
Regular tiling of a two-dimensional space
faces are the same color. Colors here represent the lattice positions. Single-color (1-tile) lattices are parallelogon hexagons. Other isohedrally-tiled
Hexagonal_tiling
System of dividing land in the United States
plat, or divide, real property for sale and settling. Also known as the Rectangular Survey System, it was created by the Land Ordinance of 1785 to survey
Public_Land_Survey_System
Vertical rectangular panels in Japanese architecture
In Japanese architecture, fusuma (襖) are vertical rectangular panels which can slide from side to side to redefine spaces within a room, or act as doors
Fusuma
Dessert pie made with apples
pastry both above and below the filling; the upper crust may be solid or latticed (woven of crosswise strips). The bottom crust may be baked separately ("blind")
Apple_pie
Interference pattern
through the intersections of the two patterns. If we consider a cell of the lattice formed, we can see that it is a rhombus with the four sides equal to d
Moiré_pattern
Interlaced decorative design
designs used to decorate objects with a grid or a lattice. Designs have developed from the rectangular wave Greek fret to intricate intertwined patterns
Fretwork
Industrial and art exhibition
hyperboloid steel tower-shell (Shukhov Tower) and the world’s first steel lattice hanging and arch-like overhead covers-shells (8 exhibition pavilions with
All-Russia_Exhibition_1896
construction [∞,2,∞] also exists, seen as two sets of parallel mirrors making a rectangular fundamental domain. If the domain is square, this symmetry can be doubled
List of Euclidean uniform tilings
List_of_Euclidean_uniform_tilings
Number of paths between grid corners, allowing diagonal steps
{\displaystyle D} counts the paths from the southwest corner (0, 0) of a rectangular grid to the northeast corner (m, n), using only single steps north, northeast
Delannoy_number
Structural system where a building is designed to act like a hollow cylinder
in New York City is also another example that adapted this system. Some lattice towers have steel tube elements, like the guyed Warsaw Radio Mast or free-standing
Tube_(structure)
United States historic place
gabled metal roof and highly decorative façade. The building is set on a lattice brick curtain wall. It was listed on the National Register of Historic
Hampton_Hendrix_Office
Optical illusion
involving informal fallacy in money number of interior lattice points number of boundary lattice points https://zenodo.org/records/20511537 Gardner, Martin
Missing_square_puzzle
Rigid structure that consists of two-force members only
lower aerodynamic drag. American architect Ithiel Town designed Town's Lattice Truss as an alternative to heavy-timber bridges. His design, patented in
Truss
Process for achieving system stability
which a random initial configuration of active cells is selected from a lattice or other space, and then cells with few active neighbors are successively
Bootstrap_percolation
Solid material with highly ordered microscopic structure
arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals
Crystal
Model in statistical mechanics generalizing the Ising model
lattice; the lattice is usually taken to be a two-dimensional rectangular Euclidean lattice, but is often generalized to other dimensions and lattice
Potts_model
Coordinate system for digital imaging
storage when compared to rectangular sampling. Researchers have shown that the hexagonal grid is the optimal sampling lattice and its use provides a sampling
Hexagonal Efficient Coordinate System
Hexagonal_Efficient_Coordinate_System
How many integer lattice points there are in a circle
the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and with radius r {\displaystyle
Gauss_circle_problem
Imaging Instrument
surface of a crystal of silicon carbide (SiC) are arranged in a hexagonal lattice and are 0.3 nm apart. STM nanomanipulation of PTCDA molecules on graphite
Scanning_tunneling_microscope
Image display as a 2D grid of pixels
graphic, raster image, or simply raster is a digital image made up of a rectangular grid of tiny colored (usually square) so-called pixels. Unlike vector
Raster_graphics
Concept in molecular modelling
Wigner-Seitz cell of certain lattice packing. For example, the hypercubic periodic boundary condition corresponds to the hypercubic lattice packing. It is then
Periodic_boundary_conditions
Figurate number
integers that can be represented as a lattice of points arranged in an equilateral triangle. The triangular lattice representing the n {\displaystyle n}
Triangular_number
Saloon car (1986–1994)
as Majestic. These cars were mostly finished in Regency Red (with Red Lattice alloys), apart from the 1992 cars which were finished in Black Cherry (with
Jaguar_XJ_(XJ40)
Spherical shell structure based on a geodesic polyhedron
A geodesic dome is a hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron. The rigid triangular elements of the dome distribute
Geodesic_dome
Positive real number which when multiplied by itself gives 7
between any two points of a cubic integer lattice (or equivalently, the length of the space diagonal of a rectangular cuboid with integer side lengths). 15
Square_root_of_7
Field of geometry closely arranging circles on a plane
highest-density lattice packing of circles is the hexagonal packing arrangement, in which the centres of the circles are arranged in a hexagonal lattice (staggered
Circle_packing
Decomposition of periodic functions
periodicity as the Bravais lattice, i.e. f ( r ) = f ( R + r ) {\displaystyle f(\mathbf {r} )=f(\mathbf {R} +\mathbf {r} )} for any lattice vector R {\displaystyle
Fourier_series
UNESCO World Heritage Site in Patan, India
accompanied by children. Cantilevered brackets in well shaft Geometric lattice patterns and designs resembling Patola textile designs There are gradually
Rani_ki_Vav
RECTANGULAR LATTICE
RECTANGULAR LATTICE
Surname or Lastname
English
English : variant of Fretter, an occupational name for a maker of ornaments (especially for the hair) consisting of jewels set in a lattice network, from an agent derivative of Middle English frette, Old French frete ‘interlaced work’.
Surname or Lastname
English
English : probably a habitational name from a lost or unidentified place, generally from a field name denoting a triangular area, Old English gÄra (see Gore) at the corner of an open field after rectangular furlongs had been laid out.Jewish : Americanized form of one or more like-sounding Jewish surnames.U.S. President James Abram Garfield (1831–81) was preceded by at least six Garfields born in America, his immigrant ancestor having come to Massachusetts Bay with John Winthrop in 1630.
RECTANGULAR LATTICE
RECTANGULAR LATTICE
Male
Russian
(ОÑип) Russian form of Greek Ioseph, OSIP means "(God) shall add (another son)."
Boy/Male
English American French Latin
Fifth. Derived from Roman clan name.
Boy/Male
Hindu, Indian, Telugu, Traditional
One who has Mouth Like an Elephant
Boy/Male
Hindu, Indian
Study
Boy/Male
Tamil
Festival, Strong
Male
Italian
Italian form of Latin Franciscus, FRANCESCO means "French."
Boy/Male
British, English
From the Island of Linden Trees
Boy/Male
Indian, Sanskrit
Regent of a Direction
Girl/Female
Indian
Praising Allah, Holy
Boy/Male
Tamil
RECTANGULAR LATTICE
RECTANGULAR LATTICE
RECTANGULAR LATTICE
RECTANGULAR LATTICE
RECTANGULAR LATTICE
a.
Containing or having two right angles; as, a birectangular spherical triangle.
n.
A rectangular figure.
n.
The quality or condition of being rectangular, or right-angled.
n.
A rectangular iron frame in which pages or columns of type are imposed.
n.
A solid of five sides, having a rectangular base, two rectangular or trapezoidal sides meeting in an edge, and two triangular ends.
a.
Having ten angles.
n.
An oblong rectangular piece of cloth, worn by Roman ladies, and fastened with brooches.
n.
A drawplate with a narrow, rectangular orifice, for drawing flat strips, as watch springs, etc.
a.
Rectangular.
a.
Right-angled; having one or more angles of ninety degrees.
a.
Having eight angles; eight-angled.
a.
Heptagonal.
a.
Rectangular.
n.
A rectangular rent made in cloth; -- called also winkle-hole.
n.
Any oblong rectangular mass; as, a brick of maple sugar; a penny brick (of bread).
a.
Having five corners or angles.
a.
Right-angled; rectangular; as, an orthogonal intersection of one curve with another.
a.
Nearly or approximately pentangular; almost pentangular.
a.
Having greater length than breadth, esp. when rectangular.
a.
Having seven angles.