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COMPLEX POLYTOPE

  • Complex polytope
  • Generalization of a polytope in real space

    In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real

    Complex polytope

    Complex_polytope

  • Polytope
  • Geometric object with flat sides

    In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any

    Polytope

    Polytope

  • Cross-polytope
  • Regular polytope dual to the hypercube in any number of dimensions

    In geometry, a cross-polytope, hyperoctahedron, orthoplex, staurotope, or cocube is a regular, convex polytope that exists in n-dimensional Euclidean

    Cross-polytope

    Cross-polytope

    Cross-polytope

  • Regular polytope
  • Polytope with highest degree of symmetry

    In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. In

    Regular polytope

    Regular polytope

    Regular_polytope

  • Regular 4-polytope
  • Four-dimensional analogues of the regular polyhedra in three dimensions

    In mathematics, a regular 4-polytope or regular polychoron is a regular four-dimensional polytope. They are the four-dimensional analogues of the regular

    Regular 4-polytope

    Regular 4-polytope

    Regular_4-polytope

  • 4 21 polytope
  • Polytope in 8-dimensional geometry

    In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group. It was discovered by Thorold Gosset

    4 21 polytope

    4 21 polytope

    4_21_polytope

  • Tesseract
  • Four-dimensional analogue of the cube

    labels it the γ4 polytope. The term hypercube without a dimension reference is frequently treated as a synonym for this specific polytope. The construction

    Tesseract

    Tesseract

    Tesseract

  • 1 22 polytope
  • Uniform 6-polytope

    122 polytope is a uniform polytope, constructed from the E6 group. It was first published in E. L. Elte's 1912 listing of semiregular polytopes, named

    1 22 polytope

    1 22 polytope

    1_22_polytope

  • Complex geometry
  • Study of complex manifolds and several complex variables

    and B Complex analytic space Complex Lie group Complex polytope Complex projective space Cousin problems Deformation Theory#Deformations of complex manifolds

    Complex geometry

    Complex_geometry

  • Witting polytope
  • In 4-dimensional complex geometry, the Witting polytope is a regular complex polytope, named as: 3{3}3{3}3{3}3, and Coxeter diagram . It has 240 vertices

    Witting polytope

    Witting polytope

    Witting_polytope

  • Convex polytope
  • Convex hull of a finite set of points in a Euclidean space

    A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n {\displaystyle n} -dimensional

    Convex polytope

    Convex polytope

    Convex_polytope

  • 5-cube
  • 5-dimensional hypercube

    (n ≥ 5), ISBN 0-486-61480-8 Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes. Cambridge University Press. ISBN 0-521-39490-2. Kaleidoscopes: Selected

    5-cube

    5-cube

  • 4-polytope
  • Four-dimensional geometric object with flat sides

    In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure

    4-polytope

    4-polytope

    4-polytope

  • 16-cell
  • Four-dimensional analog of the octahedron

    convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,4}. It is one of the six regular convex 4-polytopes first described

    16-cell

    16-cell

    16-cell

  • List of polygons, polyhedra and polytopes
  • A polytope is a geometric object with flat sides, which exists in any general number of dimensions. The following list of polygons, polyhedra and polytopes

    List of polygons, polyhedra and polytopes

    List_of_polygons,_polyhedra_and_polytopes

  • Hypercube
  • Convex polytope, the n-dimensional analogue of a square and a cube

    measure polytope (originally from Elte, 1912) is also used, notably in the work of H. S. M. Coxeter who also labels the hypercubes the γn polytopes. The

    Hypercube

    Hypercube

    Hypercube

  • 90 (number)
  • Natural number between 89 and 91

    the 4 21 {\displaystyle 4_{21}} polytope, which shares 240 vertices with the Witting polytope in four-dimensional complex space. By Coxeter, the incidence

    90 (number)

    90_(number)

  • Polyhedron
  • Flat-sided three-dimensional shape

    two-dimensional polygons and to be the three-dimensional specialization of polytopes (a more general concept in any number of dimensions). Polyhedra have several

    Polyhedron

    Polyhedron

    Polyhedron

  • Abstract polytope
  • Poset representing certain properties of a polytope

    mathematics, an abstract polytope is an algebraic partially ordered set which captures certain combinatorial properties of a traditional polytope without specifying

    Abstract polytope

    Abstract polytope

    Abstract_polytope

  • 6-cube
  • 6-dimensional hypercube

    (1991) [1974]. Regular Complex Polytopes. Cambridge University Press. ISBN 0-521-39490-2. Klitzing, Richard. "6D uniform polytopes (polypeta) with acronyms"

    6-cube

    6-cube

    6-cube

  • Complex polygon
  • Polygon in complex space, or which self-intersects

    general complex polytope in any number of complex dimensions. In a real plane, a visible figure can be constructed as the real conjugate of some complex polygon

    Complex polygon

    Complex_polygon

  • 5-cell
  • Four-dimensional analogue of the tetrahedron

    In geometry, the 5-cell is the convex 4-polytope with Schläfli symbol {3,3,3}. It is a 5-vertex four-dimensional object bounded by five tetrahedral cells

    5-cell

    5-cell

    5-cell

  • Regular complex polygon
  • Polygons which have an accompanying imaginary dimension for each real dimension

    dimensions to be visualized. A complex polygon is generalized as a complex polytope in C n {\displaystyle \mathbb {C} ^{n}} . A complex polygon may be understood

    Regular complex polygon

    Regular complex polygon

    Regular_complex_polygon

  • List of regular polytopes
  • regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank. There is only one polytope of

    List of regular polytopes

    List of regular polytopes

    List_of_regular_polytopes

  • 5-orthoplex
  • Convex regular 5-polytope in geometry

    In five-dimensional geometry, a 5-orthoplex, or 5-cross polytope, is a five-dimensional polytope with 10 vertices, 40 edges, 80 triangle faces, 80 tetrahedron

    5-orthoplex

    5-orthoplex

    5-orthoplex

  • 8-cube
  • 8-dimensional hypercube

    polytopes in n dimensions (n ≥ 5) Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes. Cambridge University Press. ISBN 0-521-39490-2. Kaleidoscopes: Selected

    8-cube

    8-cube

    8-cube

  • 22 (number)
  • Natural number

    wolfram.com. Retrieved 2022-07-02. Coxeter, H.S.M. (1991), Regular Complex Polytopes, Cambridge University Press, p. 140, ISBN 0-521-39490-2 Ambrogelly

    22 (number)

    22_(number)

  • 2 21 polytope
  • Uniform 6-polytope

    In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group. It was discovered by Thorold Gosset

    2 21 polytope

    2 21 polytope

    2_21_polytope

  • Polygon
  • Plane figure bounded by line segments

    image, Coxeter, H.S.M.; Regular Polytopes, 3rd Edn, Dover (pbk), 1973, p. 114 Shephard, G.C.; "Regular complex polytopes", Proc. London Math. Soc. Series

    Polygon

    Polygon

  • Semiregular polytope
  • Isogonal polytope with regular facets

    definition a semiregular polytope is usually taken to be a polytope that is vertex-transitive and has all its facets being regular polytopes. E.L. Elte compiled

    Semiregular polytope

    Semiregular polytope

    Semiregular_polytope

  • 7-cube
  • 7-dimensional hypercube

    Regular Polytopes, three regular polytopes in n dimensions (n ≥ 5), ISBN 0-486-61480-8 Coxeter, H.S.M. (1991) [1974]. Regular Complex Polytopes. Cambridge

    7-cube

    7-cube

    7-cube

  • Vertex (geometry)
  • Point where two or more curves, lines, or edges meet

    topological cell complex, as can the faces of a polyhedron or polytope; the vertices of other kinds of complexes such as simplicial complexes are its zero-dimensional

    Vertex (geometry)

    Vertex_(geometry)

  • Simplicial polytope
  • Polytope whose facets are all simplices

    simplicial polytopes In geometry, a simplicial polytope is a polytope whose facets are all simplices. It is topologically dual to simple polytopes. Polytopes that

    Simplicial polytope

    Simplicial polytope

    Simplicial_polytope

  • 600-cell
  • Four-dimensional analog of the icosahedron

    In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,5}. It is also known

    600-cell

    600-cell

    600-cell

  • Coxeter–Dynkin diagram
  • Pictorial representation of symmetry

    (called branches) representing a Coxeter group or sometimes a uniform polytope or uniform tiling constructed from the group. A class of closely related

    Coxeter–Dynkin diagram

    Coxeter–Dynkin diagram

    Coxeter–Dynkin_diagram

  • 5-demicube
  • Regular 5-polytope

    five-dimensional geometry, a demipenteract or 5-demicube is a semiregular 5-polytope, constructed from a 5-hypercube (penteract) with alternated vertices removed

    5-demicube

    5-demicube

    5-demicube

  • Complex reflection group
  • Concept in mathematics

    complex polytopes. In particular, they include the symmetry groups of regular real polyhedra. The Shephard groups may be characterized as the complex

    Complex reflection group

    Complex_reflection_group

  • Hessian polyhedron
  • Coxeter, Complex Regular polytopes, p.123 Coxeter Regular Convex Polytopes, 12.5 The Witting polytope Coxeter, Complex Regular polytopes, p.132 Coxeter

    Hessian polyhedron

    Hessian polyhedron

    Hessian_polyhedron

  • 24-cell
  • Regular object in four dimensional geometry

    In four-dimensional geometry, the 24-cell is a convex regular 4-polytope, a four-dimensional analogue of a Platonic solid. It is named for the 24 octahedra

    24-cell

    24-cell

    24-cell

  • Stellation
  • Extending the elements of a polytope to form a new figure

    in two dimensions, a polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure. Starting with an original figure

    Stellation

    Stellation

    Stellation

  • Quaternionic polytope
  • Concept in geometry

    ones. Similarly to complex polytopes, points are not ordered and there is no sense of "between", and thus a quaternionic polytope may be understood as

    Quaternionic polytope

    Quaternionic_polytope

  • 12 (number)
  • Natural number

    dimensions. There are twelve complex apeirotopes in dimensions five and higher, which include van Oss polytopes in the form of complex n {\displaystyle n} -orthoplexes

    12 (number)

    12_(number)

  • Simplex
  • Multi-dimensional generalization of triangle

    dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example, a 0-dimensional simplex is a point

    Simplex

    Simplex

    Simplex

  • 120-cell
  • Four-dimensional analog of the dodecahedron

    In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {5,3,3}. It is also called

    120-cell

    120-cell

    120-cell

  • Simplicial complex
  • Type of mathematical set

    simplicial complex can be thought of as a complex where all facets have the same dimension. For (boundary complexes of) simplicial polytopes this coincides

    Simplicial complex

    Simplicial complex

    Simplicial_complex

  • Petrie polygon
  • Skew polygon derived from a polytope

    In geometry, a Petrie polygon for a regular polytope of n dimensions is a skew polygon in which every n – 1 consecutive sides (but no n) belongs to one

    Petrie polygon

    Petrie polygon

    Petrie_polygon

  • 6-demicube
  • Uniform 6-polytope

    6-polytope, constructed from a 6-cube (hexeract) with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called

    6-demicube

    6-demicube

    6-demicube

  • Configuration (polytope)
  • regular polytope a special kind of configuration.[citation needed] Other configurations in geometry are something different. These polytope configurations

    Configuration (polytope)

    Configuration_(polytope)

  • Square tiling
  • Regular tiling of the Euclidean plane

    (1987), p. 473–481. Coxeter, Regular Complex Polytopes, pp. 111-112, p. 136. Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8

    Square tiling

    Square tiling

    Square_tiling

  • 3-4 duoprism
  • some of the uniform 5-polytopes in the B5 family. The quasiregular complex polytope 3{}×4{}, , in C 2 {\displaystyle \mathbb {C} ^{2}} has a real representation

    3-4 duoprism

    3-4 duoprism

    3-4_duoprism

  • 5-simplex
  • Regular 5-polytope

    In five-dimensional geometry, a 5-simplex is a self-dual regular 5-polytope. It has six vertices, 15 edges, 20 triangle faces, 15 tetrahedral cells, and

    5-simplex

    5-simplex

  • Trihexagonal tiling
  • Tiling of a plane by regular hexagons and equilateral triangles

    Mutations". CiteSeerX 10.1.1.30.8536. Coxeter, H.S.M. (1991). Regular Complex Polytopes (2nd ed.). Cambridge University Press. pp. 111–2, 136. ISBN 978-0-521-39490-1

    Trihexagonal tiling

    Trihexagonal tiling

    Trihexagonal_tiling

  • 7-simplex
  • Type of 7-polytope

    In 7-dimensional geometry, a 7-simplex is a self-dual regular 7-polytope. It has 8 vertices, 28 edges, 56 triangle faces, 70 tetrahedral cells, 56 5-cell

    7-simplex

    7-simplex

    7-simplex

  • Skew polygon
  • Polygonal chain whose vertices are not all coplanar

    Regular complex polytopes, p. 6 Abstract Regular Polytopes, p.217 McMullen, Peter; Schulte, Egon (December 2002), Abstract Regular Polytopes (1st ed.)

    Skew polygon

    Skew polygon

    Skew_polygon

  • Möbius–Kantor polygon
  • 1992 Coxeter, Complex Regular polytopes, p. 117, 132 Coxeter, Regular Complex Polytopes, p. 109 Shephard, G.C.; Regular complex polytopes, Proc. London

    Möbius–Kantor polygon

    Möbius–Kantor polygon

    Möbius–Kantor_polygon

  • Hexagonal tiling
  • Regular tiling of a two-dimensional space

    pp. 74–75, pattern 2 Coxeter, Regular Complex Polytopes, pp. 111–112, p. 136. Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8

    Hexagonal tiling

    Hexagonal tiling

    Hexagonal_tiling

  • Facet (geometry)
  • Feature of a polyhedron, polytope, etc.

    In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself

    Facet (geometry)

    Facet_(geometry)

  • List of mathematical shapes
  • needed] 142 polytope, 241 polytope, 421 polytope, Truncated 421 polytope, Truncated 241 polytope, Truncated 142 polytope, Cantellated 421 polytope, Cantellated

    List of mathematical shapes

    List_of_mathematical_shapes

  • Five-dimensional space
  • Geometric space with five dimensions

    higher dimensions, including five-dimensional space. List of regular 5-polytopes — regular geometric shapes that exist in five-dimensional space. Four-dimensional

    Five-dimensional space

    Five-dimensional space

    Five-dimensional_space

  • Triangular tiling
  • Regular tiling of the plane

    isohedral tilings, p.473-481 Coxeter, Regular Complex Polytopes, pp. 111-112, p. 136. Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8

    Triangular tiling

    Triangular tiling

    Triangular_tiling

  • Seven-dimensional space
  • Geometric space with seven dimensions

    were seven-dimensional. A polytope in seven dimensions is called a 7-polytope. The most studied are the regular polytopes, of which there are only three

    Seven-dimensional space

    Seven-dimensional_space

  • Geoffrey Colin Shephard
  • British mathematician (1927–2016)

    invariant theory of finite groups, began the study of complex polytopes, and classified the complex reflection groups. Shephard earned his Ph.D. in 1954

    Geoffrey Colin Shephard

    Geoffrey_Colin_Shephard

  • Complete bipartite graph
  • Bipartite graph where each node of 1st set is linked to all nodes of 2nd set

    Discrete Math, Springer, p. 437, ISBN 9780387941158. Coxeter, Regular Complex Polytopes, second edition, p.114 Garey, Michael R.; Johnson, David S. (1979)

    Complete bipartite graph

    Complete bipartite graph

    Complete_bipartite_graph

  • List of algebraic topology topics
  • Algebraic topology uses abstract algebra to study topological spaces

    Simplex Simplicial complex Polytope Triangulation Barycentric subdivision Simplicial approximation theorem Abstract simplicial complex Simplicial set Simplicial

    List of algebraic topology topics

    List_of_algebraic_topology_topics

  • Harold Scott MacDonald Coxeter
  • Canadian geometer (1907–2003)

    author of 12 books, including The Fifty-Nine Icosahedra (1938) and Regular Polytopes (1947). Many concepts in geometry and group theory are named after him

    Harold Scott MacDonald Coxeter

    Harold Scott MacDonald Coxeter

    Harold_Scott_MacDonald_Coxeter

  • 8-orthoplex
  • Convex regular 8-polytope

    In geometry, an 8-orthoplex or 8-cross polytope is a regular 8-polytope with 16 vertices, 112 edges, 448 triangle faces, 1120 tetrahedron cells, 1792 5-cell

    8-orthoplex

    8-orthoplex

    8-orthoplex

  • Tetrahedron
  • Polyhedron with four faces

    tetrahedron of the cube is an example of a Heronian tetrahedron. Every regular polytope, including the regular tetrahedron, has its characteristic orthoscheme

    Tetrahedron

    Tetrahedron

    Tetrahedron

  • Face (geometry)
  • Planar surface that forms part of the boundary of a solid object

    modern treatments of the geometry of polyhedra and higher-dimensional polytopes, a "face" is defined in such a way that it may have any dimension. The

    Face (geometry)

    Face (geometry)

    Face_(geometry)

  • Joint spectral radius
  • matematika. 2 (1): 205–231. Guglielmi, N.; Wirth, F.; Zennaro, M. (2005). "Complex polytope extremality results for families of matrices". SIAM Journal on Matrix

    Joint spectral radius

    Joint_spectral_radius

  • Binary tetrahedral group
  • Nonabelian group in algebraic group theory

    48 Binary icosahedral group, 2I = ⟨2,3,5⟩, order 120 Coxeter, Complex Regular Polytopes, p 109, Fig 11.5E Coxeter&Moser: Generators and Relations for

    Binary tetrahedral group

    Binary tetrahedral group

    Binary_tetrahedral_group

  • Polytope compound
  • 3D shape made of polyhedra sharing a common center

    regular polytopes. Coxeter lists a few of these in his book Regular Polytopes. McMullen added six in his paper New Regular Compounds of 4-Polytopes. Self-duals:

    Polytope compound

    Polytope_compound

  • Eight-dimensional space
  • Geometric space with eight dimensions

    geometric constructions. A polytope in eight dimensions is called an 8-polytope. The most studied are the regular polytopes, of which there are only three

    Eight-dimensional space

    Eight-dimensional_space

  • 8-simplex
  • Convex regular 8-polytope

    In geometry, an 8-simplex is a self-dual regular 8-polytope. It has 9 vertices, 36 edges, 84 triangle faces, 126 tetrahedral cells, 126 5-cell 4-faces

    8-simplex

    8-simplex

    8-simplex

  • 7-orthoplex
  • Regular 7- polytope

    In geometry, a 7-orthoplex, or 7-cross polytope, is a regular 7-polytope with 14 vertices, 84 edges, 280 triangle faces, 560 tetrahedron cells, 672 5-cell

    7-orthoplex

    7-orthoplex

    7-orthoplex

  • Regular dodecahedron
  • Solid with 12 equal pentagonal faces

    Configurations". Regular Polytopes (3rd ed.). New York: Dover Publications. Coxeter, H. S. M. (1991). Regular Complex Polytopes (2nd ed.). Cambridge: Cambridge

    Regular dodecahedron

    Regular dodecahedron

    Regular_dodecahedron

  • Hosohedron
  • Spherical polyhedron composed of lunes

     108–109. ISBN 978-0-88385-511-9. Coxeter, H.S.M. (1974). Regular Complex Polytopes. London: Cambridge University Press. p. 20. ISBN 0-521-20125-X. The

    Hosohedron

    Hosohedron

    Hosohedron

  • 7-demicube
  • Uniform 7-polytope

    In geometry, a demihepteract or 7-demicube is a uniform 7-polytope, constructed from the 7-hypercube (hepteract) with alternated vertices removed. It is

    7-demicube

    7-demicube

    7-demicube

  • Pentellated 7-cubes
  • seven-dimensional geometry, a pentellated 7-cube is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-cube. There

    Pentellated 7-cubes

    Pentellated 7-cubes

    Pentellated_7-cubes

  • Rectified 5-simplexes
  • five-dimensional geometry, a rectified 5-simplex is a convex uniform 5-polytope, being a rectification of the regular 5-simplex. There are three unique

    Rectified 5-simplexes

    Rectified 5-simplexes

    Rectified_5-simplexes

  • Infinite skew polygon
  • Non-planar polygon with infinitely many sides

    geometry, an infinite skew polygon or skew apeirogon is an infinite 2-polytope with vertices that are not all colinear. Infinite zig-zag skew polygons

    Infinite skew polygon

    Infinite_skew_polygon

  • Pentellated 7-orthoplexes
  • seven-dimensional geometry, a pentellated 7-orthoplex is a convex uniform 7-polytope with 5th order truncations (pentellation) of the regular 7-orthoplex. There

    Pentellated 7-orthoplexes

    Pentellated 7-orthoplexes

    Pentellated_7-orthoplexes

  • Discrete geometry
  • Branch of geometry that studies combinatorial properties and constructive methods

    discrete geometry. A polytope is a geometric object with flat sides, which exists in any general number of dimensions. A polygon is a polytope in two dimensions

    Discrete geometry

    Discrete geometry

    Discrete_geometry

  • 6-simplex
  • Uniform 6-polytope

    In geometry, a 6-simplex is a self-dual regular 6-polytope. It has 7 vertices, 21 edges, 35 triangle faces, 35 tetrahedral cells, 21 5-cell 4-faces, and

    6-simplex

    6-simplex

  • Dicyclic group
  • Type of cyclic group in group theory

    Coxeter, H. S. M. (1974), "7.1 The Cyclic and Dicyclic groups", Regular Complex Polytopes, Cambridge University Press, pp. 74–75. Coxeter, H. S. M.; Moser,

    Dicyclic group

    Dicyclic group

    Dicyclic_group

  • 6-orthoplex
  • Regular 6 dimensional polytope

    In geometry, a 6-orthoplex, or 6-cross polytope, is a regular 6-polytope with 12 vertices, 60 edges, 160 triangle faces, 240 tetrahedron cells, 192 5-cell

    6-orthoplex

    6-orthoplex

    6-orthoplex

  • Boerdijk–Coxeter helix
  • Linear stacking of regular tetrahedra that form helices

    Hopf fibrations. Banchoff 1989. Coxeter, H. S. M. (1974). Regular Complex Polytopes. Cambridge University Press. ISBN 052120125X. Boerdijk, A.H. (1952)

    Boerdijk–Coxeter helix

    Boerdijk–Coxeter helix

    Boerdijk–Coxeter_helix

  • Regular polyhedron
  • Polyhedron with regular congruent polygons as faces

    face, an edge of the face, a vertex of the edge, and the null polytope. An abstract polytope is said to be regular if its combinatorial symmetries are transitive

    Regular polyhedron

    Regular_polyhedron

  • Complex affine space
  • Affine space over the complex numbers

    In particular, it is a Stein manifold. Analytic space Complex coordinate space Complex polytope Exotic affine space *Berger, Marcel (1987), Geometry I

    Complex affine space

    Complex_affine_space

  • Hexicated 7-orthoplexes
  • a hexicated 7-orthoplex (also hexicated 7-cube) is a convex uniform 7-polytope, including 6th-order truncations (hexication) from the regular 7-orthoplex

    Hexicated 7-orthoplexes

    Hexicated 7-orthoplexes

    Hexicated_7-orthoplexes

  • Ehrhart polynomial
  • Relation of an integral polytope's volume to how many integer points it encloses

    mathematics, an integral polytope has an associated Ehrhart polynomial that encodes the relationship between the volume of a polytope and the number of integer

    Ehrhart polynomial

    Ehrhart_polynomial

  • Barycentric subdivision
  • Method for dividing a simplicial complex

    convex polytope of the same dimension. In this version of barycentric subdivision, it is not necessary for the polytope to form a simplicial complex: it

    Barycentric subdivision

    Barycentric subdivision

    Barycentric_subdivision

  • 3-3 duoprism
  • duoprism or triangular duoprism is a four-dimensional convex polytope. The duoprism is a 4-polytope that can be constructed using Cartesian product of two polygons

    3-3 duoprism

    3-3 duoprism

    3-3_duoprism

  • Point groups in three dimensions
  • Groups of point isometries in 3 dimensions

    Coxeter, H. S. M. (1974), "7 The Binary Polyhedral Groups", Regular Complex Polytopes, Cambridge University Press, pp. 73–82. Coxeter, H. S. M. & Moser

    Point groups in three dimensions

    Point_groups_in_three_dimensions

  • H-vector
  • algebraic combinatorics, the h-vector of a simplicial polytope is a fundamental invariant of the polytope which encodes the number of faces of different dimensions

    H-vector

    H-vector

  • Cairo pentagonal tiling
  • Tiling of the plane by pentagons

    art for the 1974 first edition of H. S. M. Coxeter's book Regular Complex Polytopes. O'Keeffe, M.; Hyde, B. G. (1980), "Plane nets in crystal chemistry"

    Cairo pentagonal tiling

    Cairo pentagonal tiling

    Cairo_pentagonal_tiling

  • Square
  • Shape with four equal sides and angles

    truncated square is an octagon. The square belongs to a family of regular polytopes that includes the cube in three dimensions and the hypercubes in higher

    Square

    Square

    Square

  • Runcinated 7-orthoplexes
  • seven-dimensional geometry, a runcinated 7-orthoplex is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-orthoplex. There

    Runcinated 7-orthoplexes

    Runcinated 7-orthoplexes

    Runcinated_7-orthoplexes

  • Möbius–Kantor configuration
  • Geometric structure of 8 points and 8 lines

    Coxeter, H. S. M.; Shephard, G. C. (1992), "Portraits of a family of complex polytopes", Leonardo, 25 (3/4): 239, doi:10.2307/1575843, JSTOR 1575843. Reprinted

    Möbius–Kantor configuration

    Möbius–Kantor configuration

    Möbius–Kantor_configuration

  • 5 21 honeycomb
  • Type of uniform tessellation

    ∪ Using a complex number coordinate system, it can also be constructed as a C 4 {\displaystyle \mathbb {C} ^{4}} regular complex polytope, given the

    5 21 honeycomb

    5_21_honeycomb

  • Cayley–Dickson construction
  • Method for producing composition algebras

    produced by this process are known as Cayley–Dickson algebras, for example complex numbers, quaternions, and octonions. These examples are useful composition

    Cayley–Dickson construction

    Cayley–Dickson_construction

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Online names & meanings

  • Wendy
  • Girl/Female

    German American English

    Wendy

    Family; Wanderer.

  • Bhajndeep
  • Boy/Male

    Indian, Punjabi, Sikh

    Bhajndeep

    Devotional Lamp

  • Ellina
  • Girl/Female

    Finnish, French, German

    Ellina

    Bright; All; Completely

  • Vanani
  • Girl/Female

    Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu

    Vanani

    Forest

  • Kaleigh
  • Girl/Female

    English American

    Kaleigh

    and Kayla, meaning: keeper of the keys; pure.

  • Norwich
  • Surname or Lastname

    English

    Norwich

    English : habitational name from the city of Norwich in East Anglia, named from Old English north ‘north’ + wīc ‘trading center’, ‘harbor’, or a topographic name with the same meaning.

  • Rafik
  • Boy/Male

    Arabic, Hindu, Indian, Muslim

    Rafik

    Lord; Friend; Singer

  • Gursheen
  • Girl/Female

    Indian, Sikh

    Gursheen

    Guru's Pride; Reflection of Guru

  • Raxit
  • Boy/Male

    Hindu, Indian

    Raxit

    Protector; Guard

  • Saumil
  • Boy/Male

    Hindu

    Saumil

    Love to Meet different persons, A friend

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Other words and meanings similar to

COMPLEX POLYTOPE

AI search in online dictionary sources & meanings containing COMPLEX POLYTOPE

COMPLEX POLYTOPE

  • Couple
  • a.

    That which joins or links two things together; a bond or tie; a coupler.

  • Couple
  • a.

    See Couple-close.

  • Decomplex
  • a.

    Repeatedly compound; made up of complex constituents.

  • Incomplex
  • a.

    Not complex; uncompounded; simple.

  • Complete
  • a.

    Finished; ended; concluded; completed; as, the edifice is complete.

  • Couplet
  • n.

    Two taken together; a pair or couple; especially two lines of verse that rhyme with each other.

  • Coupled
  • imp. & p. p.

    of Couple

  • Complex
  • n.

    Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.

  • Complexly
  • adv.

    In a complex manner; not simply.

  • Compiled
  • imp. & p. p.

    of Compile

  • Complexus
  • n.

    A complex; an aggregate of parts; a complication.

  • Complied
  • imp. & p. p.

    of Comply

  • Coupler
  • n.

    One who couples; that which couples, as a link, ring, or shackle, to connect cars.

  • Complier
  • n.

    One who complies, yields, or obeys; one of an easy, yielding temper.

  • Compiler
  • n.

    One who compiles; esp., one who makes books by compilation.

  • Couple
  • a.

    One of the pairs of plates of two metals which compose a voltaic battery; -- called a voltaic couple or galvanic couple.

  • Complete
  • v. t.

    To bring to a state in which there is no deficiency; to perfect; to consummate; to accomplish; to fulfill; to finish; as, to complete a task, or a poem; to complete a course of education.

  • Implex
  • a.

    Intricate; entangled; complicated; complex.

  • Couple-closes
  • pl.

    of Couple-close

  • Complexed
  • a.

    Complex, complicated.