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Topics referred to by the same term
The term triangular coordinates may refer to any of at least three related systems of coordinates in the Euclidean plane: a special case of barycentric
Triangular_coordinates
Relationship between two numbers of the same kind
expressed in extended ratio form as triangular coordinates. In barycentric coordinates, a point with coordinates α, β, γ is the point upon which a weightless
Ratio
Coordinate system that is defined by points instead of vectors
Barycentric coordinates may be easily extended to three dimensions. The 3D simplex is a tetrahedron, a polyhedron having four triangular faces and four
Barycentric_coordinate_system
3D model's surface projected to a 2D image
process for texture mapping a 3D model by projecting the model's surface coordinates onto a 2D image. The letters "U" and "V" denote the axes of the 2D texture
UV_mapping
Geometric prism
vertex coordinates, permuting first 3 coordinates: ([±1,0,0]; ±1) The octahedral prism consists of two octahedra connected to each other via 8 triangular prisms
Octahedral_prism
92nd Johnson solid (20 faces)
In geometry, the triangular hebesphenorotunda is a Johnson solid with 13 equilateral triangles, 3 squares, 3 regular pentagons, and 1 regular hexagon,
Triangular_hebesphenorotunda
Tent function, often used in signal processing
A triangular function (also known as a triangle function, hat function, or tent function) is a function whose graph takes the shape of a triangle. Often
Triangular_function
with the cells of the dual 24-cell, 96 triangular prisms, and 96 hexagonal prisms. The Cartesian coordinates of an origin-centered runcitruncated 24-cell
Runcinated_24-cells
Representation of a surface as a triangle mesh with elevated vertices
three-dimensional coordinates ( x , y , z ) {\displaystyle (x,y,z)} that are arranged in a network of non-overlapping triangles. A TIN comprises a triangular network
Triangulated irregular network
Triangulated_irregular_network
Polyhedron with 20 faces
be referred to as regular icosahedra, characterized by 30 edges and 20 triangular faces. The term "regular icosahedron" generally refers to a convex polyhedron
Icosahedron
prisms), and triangular prisms (edge figure prisms). The same process applied to a 16-cell also yields the same figure. The Cartesian coordinates of the vertices
Runcinated_tesseracts
Shape with three sides
generalized notion of triangles known as the simplex, and the polytopes with triangular facets known as the simplicial polytopes. Each triangle has many special
Triangle
Four-dimensional geometrical object
cuboctahedron being dissected by a central hexagon into two triangular cupola. The Cartesian coordinates of the vertices of an origin-centered runcinated 5-cell
Runcinated_5-cell
Triangle inequality Triangular bipyramid Triangular prism Triangular pyramid Triangular tiling Triangulation Trilinear coordinates Trilinear polarity Trisected
List_of_triangle_topics
Solid with four equal triangular faces
A regular tetrahedron is a polyhedron with four equilateral triangular faces. A regular tetrahedron is a tetrahedron (that is, a four-sided polyhedron)
Regular_tetrahedron
Polyhedron with four faces
tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices
Tetrahedron
of the dual 24-cell, and 96 triangular prisms corresponding with the edges of the first 24-cell. The Cartesian coordinates of a cantitruncated 24-cell
Cantellated_24-cells
Graph whose embedding in a Euclidean space forms a regular tiling
to the points in the plane with integer coordinates, x-coordinates being in the range 1, ..., n, y-coordinates being in the range 1, ..., m, and two vertices
Lattice_graph
Coordinate system based on distances from a triangle's sidelines
In geometry, the trilinear coordinates x : y : z of a point relative to a given triangle describe the relative directed distances from the three sidelines
Trilinear_coordinates
Numbers arranged in a triangle
Storing a triangular array in a computer requires a mapping from the two-dimensional coordinates (i, j) to a linear memory address. If two triangular arrays
Triangular_array
Mathematical tree of cycles
problem in mathematics Are all triangular cacti graceful or nearly graceful? More unsolved problems in mathematics A triangular cactus is a special type of
Cactus_graph
Solid made by joining an n- and 2n-gon with triangles and squares
squares, while the base and its opposite face are regular polygons, the triangular, square, and pentagonal cupolae all count among the Johnson solids, and
Cupola_(geometry)
Polyhedron formed by joining two prisms
two triangular prisms; these prisms are elementaries because they cannot be sliced into many convex, regular-faced polyhedra. Cartesian coordinates for
Gyrobifastigium
Four-dimensional analogue of the tetrahedron
5-cell itself. Its maximal intersection with 3-dimensional space is the triangular prism. Its dichoral angle between cells is arccos 1/4 ≈ 75.52°. Its
5-cell
Roughly triangular basin that is the deepest part of the Gulf of Mexico
Names Advisory Committee on Undersea Features Gazetteer) is a roughly triangular basin that is the deepest part of the Gulf of Mexico named for Charles
Sigsbee_Deep
Polyhedron with 12 faces
sides=712⋅Long side The eight vertices of a cube have the coordinates (±1, ±1, ±1). The coordinates of the 12 additional vertices are (0, ±(1 + h), ±(1 −
Dodecahedron
Quasiregular space-filling tesselation
creating a nonuniform honeycomb consisting of tetrahedra and octahedra (as triangular antiprisms). Its vertex figure is an order-3 truncated triakis tetrahedron
Tetrahedral-octahedral honeycomb
Tetrahedral-octahedral_honeycomb
Any of the five regular polyhedra
the regular tetrahedron (four triangular faces), the cube (six square faces), the regular octahedron (eight triangular faces), the regular dodecahedron
Platonic_solid
Polyhedral compound
arrangement of 4 triangular prisms, aligned with the axes of three-fold rotational symmetry of an octahedron. Cartesian coordinates for the vertices of
Compound of four triangular prisms
Compound_of_four_triangular_prisms
Barycentric plot on three variables
ternary plot correspond (up to a constant) to its trilinear coordinates or barycentric coordinates. There are three equivalent methods that can be used to
Ternary_plot
Dense arrangement of congruent spheres in an infinite, regular arrangement
first row and that their y- and z-coordinates are simply r, so that their surfaces rest on the zero-planes. Coordinates of the centers of the first row
Close-packing of equal spheres
Close-packing_of_equal_spheres
Archimedean solid with 62 faces
types of regular polygon faces. It has a total of 62 faces: 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, with 60 vertices
Rhombicosidodecahedron
Folly in Rushton, Northamptonshire, England
The Triangular Lodge is a folly, designed by Sir Thomas Tresham and constructed between 1593 and 1597 near Rushton, Northamptonshire, England. It is now
Rushton_Triangular_Lodge
Convex polyhedron with 14 triangle faces
elementary polyhedra. One possible system of Cartesian coordinates for the vertices of a triaugmented triangular prism, giving it edge length 2, is: (0,23,±1)
Triaugmented_triangular_prism
centroid coordinates ( x ¯ , y ¯ ) {\displaystyle ({\bar {x}},{\bar {y}})} are given: Where the centroid coordinates are marked as zero, the coordinates are
List_of_centroids
Catalan solid with 60 faces
12 pentagonal faces of the snub dodecahedron, and triangular pyramids are added to the 20 triangular faces that do not share an edge with a pentagon. The
Pentagonal_hexecontahedron
Partition of a surface into contiguous cells
currently in use, including grids based on "square" or "rectangular" cells, triangular grids or meshes, hexagonal grids, and grids based on diamond-shaped cells
Grid_(spatial_index)
Uniform star polyhedron with 112 faces
vertices. It is given a Schläfli symbol sr{⁵/₃,³/₂}. The 40 non-snub triangular faces form 20 coplanar pairs, forming star hexagons that are not quite
Small retrosnub icosicosidodecahedron
Small_retrosnub_icosicosidodecahedron
Colour space defined by the CIE in 1931
is balanced for the equi-energy stimulus: it has coordinates (1,1,1) in both RGB and XYZ coordinates. While the above matrix is exactly specified in standards
CIE_1931_color_space
Polytope in 8-dimensional geometry
combination of signs and an arbitrary permutation of coordinates, and 128 roots (27) with coordinates obtained from ( ± 1 , ± 1 , ± 1 , ± 1 , ± 1 , ± 1
4_21_polytope
10.1017/mag.2020.115 Scott, J. A. "Some examples of the use of areal coordinates in triangle geometry", Mathematical Gazette 83, November 1999, 472–477
List_of_triangle_inequalities
Convex uniform 4-polytope
cubes, the separating edges form the three parallel edges of a triangular prism—32 triangular prisms, since there were 32 edges. Further, since each vertex
Cantellated_tesseract
vertex joins three truncated octahedra and one cube, in an equilateral triangular pyramid vertex figure. The truncated 24-cell can be constructed from polytopes
Truncated_24-cells
Polyhedron with 62 faces
its edge arrangement with the great dodecicosidodecahedron (having the triangular and pentagrammic faces in common), and the great rhombidodecahedron (having
Nonconvex great rhombicosidodecahedron
Nonconvex_great_rhombicosidodecahedron
Catalan solid with 60 faces
triakis icosahedron. The triakis icosahedron can be formed by gluing triangular pyramids to each face of a regular icosahedron. Depending on the height
Triakis_icosahedron
4-D object; direct sum of a cube and a segment
attached with two square pyramids, creating 12 square pyramidal cells, 30 triangular faces, 28 edges, and 10 vertices. A cubical bipyramid can be seen as two
Cubical_bipyramid
found, which is not always the case. For example, the land surveyor of a triangular field might find it relatively easy to measure the length of each side
Area_of_a_triangle
Four-dimensional analog of the icosahedron
tetrahedral cells with 20 meeting at each vertex. Together they form 1200 triangular faces, 720 edges, and 120 vertices. It is the 4-dimensional analogue of
600-cell
Convex polyhedron with 12 triangular faces
different approaches. This shape is also called Siamese dodecahedron, triangular dodecahedron, trigonal dodecahedron, or dodecadeltahedron. The snub disphenoid
Snub_disphenoid
triangle, and a square, with all three towers being shaped as a cylinder, a triangular prism, and a square box. These shapes make up the Azrieli Center logo
Azrieli_Center
triangular prisms. Each vertex is surrounded by 2 cuboctahedra, 2 triangular prisms, and 1 octahedron; the vertex figure is a nonuniform triangular prism
Cantellated_5-cell
Geography of Ethiopia
Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) The extreme
Extreme_points_of_Ethiopia
Convex polytope of parenthesizations
triaugmented triangular prism. Initially Jim Stasheff considered these objects as curvilinear polytopes. Subsequently, they were given coordinates as convex
Associahedron
Polyhedron with 8 triangles and 6 squares
cuboctahedron, rectified cube, or rectified octahedron is a polyhedron with 8 triangular faces and 6 square faces. A cuboctahedron has 12 identical vertices, with
Cuboctahedron
Type of tesseract
form truncated tetrahedra which share their triangular faces with each other. The Cartesian coordinates of the vertices of a bitruncated tesseract having
Truncated_tesseract
Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) Derbyshire
Listed buildings in Tintwistle
Listed_buildings_in_Tintwistle
Solid with eight equal triangular faces
dihedral angle of a regular octahedron is the angle between its two adjacent triangular faces. The angle can be obtained from the dihedral angle of an equilateral
Regular_octahedron
Number used to approximate the square root of 2
approximate the square root of two, Pell numbers can be used to find square triangular numbers, to construct integer approximations to the right isosceles triangle
Pell_number
Nonconvex uniform polyhedron with 26 faces
shares its edge arrangement with the great cubicuboctahedron (having the triangular faces and 6 square faces in common), and with the great rhombihexahedron
Nonconvex great rhombicuboctahedron
Nonconvex_great_rhombicuboctahedron
Catalan solid with 24 faces
added to the six square faces of the snub cube, and triangular pyramids are added to the eight triangular faces that do not share an edge with a square. The
Pentagonal_icositetrahedron
File format for 3D printing and scanning
specification, all STL coordinates were required to be positive numbers, but this restriction is no longer enforced and negative coordinates are commonly encountered
STL_(file_format)
Matrix decomposition
matrix A into a product A = QR of an orthonormal matrix Q and an upper triangular matrix R. QR decomposition is often used to solve the linear least squares
QR_decomposition
Triangular arrangement joining three rail lines
terminology, a wye (like the 'Y' glyph) or triangular junction (often shortened to just triangle) is a triangular joining arrangement of three rail lines
Wye_(rail)
Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) Denotes
List of longwave radio broadcasters
List_of_longwave_radio_broadcasters
Surveying method
networks are free of the strength of figure considerations that happen in triangular systems; Scale error does not add up as the traverse is performed. Azimuth
Traverse_(surveying)
Catalan solid with 60 faces
\phi ,\pm 1/\phi ,0)} and cyclic permutations of these coordinates. Multiplying all coordinates of the icosahedron by a factor of ( 3 ϕ + 12 ) / 19 ≈ 0
Pentakis_dodecahedron
Polyhedron with 32 faces
t{3,5⁄2} or t0,1{3,5⁄2} as a truncated great icosahedron. Cartesian coordinates for the vertices of a truncated great icosahedron centered at the origin
Truncated_great_icosahedron
Castle
The Venetian Triangular Castle (Albanian: Kalaja Trekëndore Venedikase) is a castle near Butrint. The castle is located by the Channel of Vivari nearby
Venetian_Triangular_Castle
18th-century fortifications of Riga
The Triangular Bastion (Latvian: Triangula bastions) was part of the 18th-century fortifications of Riga. Its foundations are nowadays visible under a
Triangular_Bastion
Lok Sabha Constituency in Delhi
Tight Triangular Contest in Purvanchali-Dominated North East Delhi". NewsClick. 11 May 2019. Retrieved 22 May 2019. "Elections 2019: Tight Triangular Contest
North East Delhi Lok Sabha constituency
North_East_Delhi_Lok_Sabha_constituency
Polyhedral compound
seen as either a polyhedral stellation or a compound. The 14 Cartesian coordinates of the vertices of the compound are. 6: (±2, 0, 0), ( 0, ±2, 0), ( 0
Compound of cube and octahedron
Compound_of_cube_and_octahedron
Similarity measure for number sequences
Euclidean distance dist(𝐀,𝐁)=2(1−SC(A,B))=2sin(θ/2). Alternatively, the triangular inequality that does work for angular distances can be expressed directly
Cosine_similarity
Empirical study of systems in transformation
entropy — negentropy. Cloud Nine Dymaxion house Quadray coordinates Tensegrity Trilinear coordinates Synergetics, http://www.rwgrayprojects.com/synergetics/synergetics
Synergetics_(Fuller)
Regular object in four dimensional geometry
six meeting at each vertex, and three at each edge. Together, it has 96 triangular faces, 96 edges, and 24 vertices. Like other four-dimensional regular
24-cell
Fragments of tapestry discovered in the Oseberg ship burial in Norway
These graves could be created in a variety of forms such as, circular, triangular, oval, or in the shape of a boat. Sometimes they were surrounded by stones
Oseberg_tapestry_fragments
Index of lists with the same name
Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) Pegla
List_of_flatiron_buildings
Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) Canada
List of areas disputed by Canada and the United States
List_of_areas_disputed_by_Canada_and_the_United_States
Probable impact crater in New Jersey, USA
Since impact, sediment filled part of the crater, giving it its present triangular shape. List of possible impact structures on Earth Rajmon, D. "Impact
Toms_Canyon_impact_crater
Mathematical description of quantum state
of x, y- and z-axis, or a choice of curvilinear coordinates as exemplified by the spherical coordinates used for the Hydrogen atomic wave functions. This
Wave_function
Polyhedral compromise map projection
map, the Airocean World Map, based on an icosahedron with a few of the triangular faces cut to avoid breaks in landmasses. The Dymaxion projection is intended
Dymaxion_map
Shape with three equal sides
concept in satellite geodesy. The two tessellation's instances are the triangular tiling where six equilateral triangles surrounds a common vertex, and
Equilateral_triangle
faces (120 triangles and 90 squares), 180 cells (60 tetrahedra and 120 triangular prisms) and 62 4-faces (12 5-cells, 30 tetrahedral prisms and 20 3-3 duoprisms)
Stericated_5-simplexes
City in Karak Governorate, Jordan
216 people (2005) was formed around the castle. The town is built on a triangular plateau with the castle at its narrow southern tip. Al-Karak has been
Al-Karak
Polyhedral compound
It's composed of a symmetric arrangement of 4 octahedra, considered as triangular antiprisms. It can be constructed by superimposing four identical octahedra
Compound_of_four_octahedra
Periodic set of points
consists of all points ( a , b ) {\displaystyle (a,b)} in the plane whose coordinates are both integers, and its higher-dimensional analogues, the integer
Lattice_(group)
to each other at their hexagonal faces, and to the tetrahedra at their triangular faces. Seen in a configuration matrix, all incidence counts between elements
Truncated_5-cell
American Civil War battle-site
The Gettysburg Battlefield is the area of the July 1–3, 1863, military engagements of the Battle of Gettysburg in and around Gettysburg, Pennsylvania.
Gettysburg_Battlefield
Polyhedral compound
with a 2n-prism, and exist as two alternated set of vertices. Cartesian coordinates for the vertices of an antiprism with n-gonal bases and isosceles triangles
Prismatic compound of antiprisms
Prismatic_compound_of_antiprisms
Equations of motion for viscous fluids
time-dependent and convective components (also the effects of non-inertial coordinates if present). The right side of the equation is in effect a summation
Navier–Stokes_equations
88th Johnson solid (18 faces)
refers to a crownlike complex of 12 triangles, contrasted with the smaller triangular complex that makes the sphenocorona. By joining both complexes, the resulting
Sphenomegacorona
Generalization of definite integrals to functions of multiple variables
transformation to polar coordinates (see the example in the picture) which means that the generic points P(x, y) in Cartesian coordinates switch to their respective
Multiple_integral
Multi-dimensional generalization of triangle
presentations is the behavior under permuting coordinates – the standard simplex is stabilized by permuting coordinates, while permuting elements of the "ordered
Simplex
Algorithm for generating contour lines on a 2D scalar field
topological grid, but the spatial coordinates assigned to the vertices can be in 2D, 3D or higher dimensions. For example, a triangular mesh may represent a 2D
Marching_squares
River in Quebec, Canada
Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) Lake Aylmer
Bernier River (Saint-François River tributary)
Bernier_River_(Saint-François_River_tributary)
State of Sudan
census, and officially estimated at 7,993,900 in 2018. It contains the Triangular capital consisting of the capital and largest city by population, Khartoum
Khartoum_State
Footpath in Wales
Map all coordinates using OpenStreetMap Download coordinates as: KML GPX (all coordinates) GPX (primary coordinates) GPX (secondary coordinates) Official
Three Castles Walk, Monmouthshire
Three_Castles_Walk,_Monmouthshire
Polygon shape with eight sides
{16}. A 3D analog of the octagon can be the rhombicuboctahedron with the triangular faces on it like the replaced edges, if one considers the octagon to be
Octagon
German mathematician (1800–1834)
der dreyeckigen Pyramide ("Foundations of the analytic theory of the triangular pyramid") "Feuerbach". sfabel.tripod.com. Retrieved 2020-07-21. Works
Karl_Wilhelm_Feuerbach
Archimedean solid with 26 faces
similar name: the nonconvex great rhombicuboctahedron. The Cartesian coordinates for the vertices of a truncated cuboctahedron having edge length 2 and
Truncated_cuboctahedron
Skyscraper in Manhattan, New York
the Fuller Building) is a 22-story, 307-foot-tall (93.6 m) steel-framed triangular building at 175 Fifth Avenue in the Flatiron District neighborhood of
Flatiron_Building
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TRIANGULAR COORDINATES
TRIANGULAR COORDINATES
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TRIANGULAR COORDINATES
TRIANGULAR COORDINATES
TRIANGULAR COORDINATES
TRIANGULAR COORDINATES
TRIANGULAR COORDINATES
TRIANGULAR COORDINATES
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