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POLYHEDRAL COMPLEX

  • Polyhedral complex
  • Math concept

    mathematics, a polyhedral complex is a set of polyhedra in a real vector space that fit together in a specific way. Polyhedral complexes generalize simplicial

    Polyhedral complex

    Polyhedral_complex

  • Tropical geometry
  • Skeletonized version of algebraic geometry

    an irreducible tropical variety if it is the support of a weighted polyhedral complex of pure dimension d that satisfies the zero-tension condition and

    Tropical geometry

    Tropical geometry

    Tropical_geometry

  • Topology
  • Branch of mathematics

    to a unique complex one, and 4-dimensional topology can be studied from the point of view of complex geometry in two variables (complex surfaces), though

    Topology

    Topology

    Topology

  • Polyhedron
  • Flat-sided three-dimensional shape

    known as polyhedral compounds. Polyhedra can be generalized into infinitely many faces called apeirohedra, the underlying space of which is a complex Hilbert

    Polyhedron

    Polyhedron

    Polyhedron

  • Fan
  • Topics referred to by the same term

    structure to describe polygons in computer graphics Fan, a type of polyhedral complex One of several types of fan-shaped deposits of sediment caused by

    Fan

    Fan

  • Cubical complex
  • } as a face of dimension − 1 {\textstyle -1} . A cubed complex is a metric polyhedral complex all of whose cells are unit cubes; more technically, it

    Cubical complex

    Cubical complex

    Cubical_complex

  • Interior (topology)
  • Largest open subset of some given set

    \operatorname {int} \mathbb {Q} =\varnothing .} If X {\displaystyle X} is the complex plane C , {\displaystyle \mathbb {C} ,} then int ⁡ ( { z ∈ C : | z | ≤

    Interior (topology)

    Interior (topology)

    Interior_(topology)

  • Boundary (topology)
  • All points in the topological closure not belonging to the interior

    slightly different concept from the boundary of a manifold or of a simplicial complex. For example, the boundary of an open disk viewed as a manifold is empty

    Boundary (topology)

    Boundary (topology)

    Boundary_(topology)

  • General topology
  • Branch of topology

    on Rn the basic open sets are the open balls. Similarly, C, the set of complex numbers, and Cn have a standard topology in which the basic open sets are

    General topology

    General topology

    General_topology

  • Zonotope
  • Minkowsi sum of line segments

    Z} , given by a zonotopal tiling of Z {\displaystyle Z} , i.e., a polyhedral complex with support Z {\displaystyle Z} : the union of all zonotopes in the

    Zonotope

    Zonotope

  • Euler characteristic
  • Topological invariant in mathematics

    In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré

    Euler characteristic

    Euler_characteristic

  • Simplicial complex
  • Type of mathematical set

    a complex where all facets have the same dimension. For (boundary complexes of) simplicial polytopes this coincides with the meaning from polyhedral combinatorics

    Simplicial complex

    Simplicial complex

    Simplicial_complex

  • Compound of five cubes
  • Polyhedral compound

    these, it can form polyhedral compounds that can also be considered as degenerate uniform star polyhedra; respectively, the small complex rhombicosidodecahedron

    Compound of five cubes

    Compound of five cubes

    Compound_of_five_cubes

  • Geodesic
  • Straight path on a curved surface or a Riemannian manifold

    often not manifolds include metric graphs, (locally compact) metric polyhedral complexes, infinite-dimensional pre-Hilbert spaces, and real trees. In a Riemannian

    Geodesic

    Geodesic

    Geodesic

  • CW complex
  • Type of topological space

    In mathematics, and specifically in topology, a CW complex (also cellular complex or cell complex) is a topological space that is built by gluing together

    CW complex

    CW_complex

  • Coarse structure
  • Concept in geometry and topology

    second-countable Homotopy homotopy group fundamental group Simplicial complex CW complex Polyhedral complex Manifold topological smooth Bundle (mathematics) Cobordism

    Coarse structure

    Coarse_structure

  • List of map projections
  • and not based on a particular projection Polyhedral maps Polyhedral maps can be folded up into a polyhedral approximation to the sphere, using particular

    List of map projections

    List_of_map_projections

  • Closure (topology)
  • All points and limit points in a subset of a topological space

    dense in R . {\displaystyle \mathbb {R} .} If X {\displaystyle X} is the complex plane C = R 2 , {\displaystyle \mathbb {C} =\mathbb {R} ^{2},} then cl

    Closure (topology)

    Closure_(topology)

  • Hyperbolization procedures
  • Topology procedure in mathematics

    A hyperbolization procedure is a procedure that turns a polyhedral complex K {\displaystyle K} into a non-positively curved space H ( K ) {\displaystyle

    Hyperbolization procedures

    Hyperbolization_procedures

  • List of general topology topics
  • covering dimension Lebesgue's number lemma Polytope Simplex Simplicial complex CW complex Manifold Triangulation Barycentric subdivision Sperner's lemma Simplicial

    List of general topology topics

    List_of_general_topology_topics

  • Function of several complex variables
  • Type of mathematical functions

    holomorphic convexity. The proof method uses an approximation by the polyhedral domain, as in Oka-Weil theorem. Note that the Riemann extension theorem

    Function of several complex variables

    Function_of_several_complex_variables

  • Möbius strip
  • Non-orientable surface with one edge

    that a longer strip would be. The Möbius strip can also be embedded as a polyhedral surface in space or flat-folded in the plane, with only five triangular

    Möbius strip

    Möbius strip

    Möbius_strip

  • Polyhedral space
  • Metric space

    Polyhedral space is a certain metric space. A (Euclidean) polyhedral space is a (usually finite) simplicial complex in which every simplex has a flat

    Polyhedral space

    Polyhedral_space

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

    In geometry, a polyhedral compound is a figure that is composed of several polyhedra sharing a common centre. They are the three-dimensional analogs of

    Polytope compound

    Polytope_compound

  • Convergence space
  • Generalization of the notion of convergence that is found in general topology

    second-countable Homotopy homotopy group fundamental group Simplicial complex CW complex Polyhedral complex Manifold topological smooth Bundle (mathematics) Cobordism

    Convergence space

    Convergence_space

  • Shelling (topology)
  • Mathematical concept

    shellable. Note that here, shellability is generalized to the case of polyhedral complexes (that are not necessarily simplicial). There is an unshellable triangulation

    Shelling (topology)

    Shelling_(topology)

  • Initial topology
  • Coarsest topology making certain functions continuous

    second-countable Homotopy homotopy group fundamental group Simplicial complex CW complex Polyhedral complex Manifold topological smooth Bundle (mathematics) Cobordism

    Initial topology

    Initial_topology

  • Silsesquioxane
  • Molecular compound with applications in ceramics

    condensed polyhedral oligomeric silsesquioxanes (POSS-mono-ol, POSS-diol and POSS-triol): Hydrogen-bonded interaction and host–guest complex". J. Organomet

    Silsesquioxane

    Silsesquioxane

    Silsesquioxane

  • Final topology
  • Finest topology making some functions continuous

    second-countable Homotopy homotopy group fundamental group Simplicial complex CW complex Polyhedral complex Manifold topological smooth Bundle (mathematics) Cobordism

    Final topology

    Final_topology

  • Tight span
  • Notion in metric geometry

    dimension n. On the other hand, if we consider the dimension of T(X) as a polyhedral complex, Develin (2006) showed that, with a suitable general position assumption

    Tight span

    Tight_span

  • Stellated octahedron
  • Polyhedral compound

    tetrahedra form the simplest of the five regular polyhedral compounds, and the only regular polyhedral compound composed of only two polyhedra. Their union

    Stellated octahedron

    Stellated octahedron

    Stellated_octahedron

  • List of polyhedral stellations
  • star polyhedra in 14th century Europe, a proper mathematical account of polyhedral stellations was given by Johannes Kepler in his 1619 classic work, Harmonices

    List of polyhedral stellations

    List_of_polyhedral_stellations

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

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

    Point groups in three dimensions

    Point_groups_in_three_dimensions

  • Toric variety
  • Algebraic variety containing an algebraic torus

    {\displaystyle \sigma } .[further explanation needed] A (polyhedral) fan is a collection of (polyhedral) cones closed under taking intersections and faces.

    Toric variety

    Toric_variety

  • Frameworks supporting the polyhedral model
  • Use of the polyhedral model (also called the polytope model) within a compiler requires software to represent the objects of this framework (sets of integer-valued

    Frameworks supporting the polyhedral model

    Frameworks_supporting_the_polyhedral_model

  • Polyhedral skeletal electron pair theory
  • Electron counting rules

    In chemistry the polyhedral skeletal electron pair theory (PSEPT) provides electron counting rules useful for predicting the structures of clusters such

    Polyhedral skeletal electron pair theory

    Polyhedral_skeletal_electron_pair_theory

  • Michael W. Davis
  • American mathematician (born 1949)

    2025 an international conference on the geometry and topology of polyhedral complexes was held in honor of his 75th birthday at Ohio State. Davis has worked

    Michael W. Davis

    Michael W. Davis

    Michael_W._Davis

  • Meadowcroft Rockshelter
  • Archaeological site near Avella, Pennsylvania, US

    complex is further defined by surveys done in the Cross Creek watershed, where other lanceolate points, small prismatic blades, and small polyhedral blade

    Meadowcroft Rockshelter

    Meadowcroft Rockshelter

    Meadowcroft_Rockshelter

  • Small complex icosidodecahedron
  • In geometry, the small complex icosidodecahedron is a degenerate uniform star polyhedron. Its edges are doubled, making it degenerate. The star has 32

    Small complex icosidodecahedron

    Small complex icosidodecahedron

    Small_complex_icosidodecahedron

  • Polyhedral symbol
  • Symbol used in coordination chemistry

    The polyhedral symbol is sometimes used in coordination chemistry and crystallography to indicate the approximate coordination geometry around the central

    Polyhedral symbol

    Polyhedral_symbol

  • Weaire–Phelan structure
  • Mathematical foam of equal-volume bubbles

    \arccos(-{\tfrac {1}{3}})\approx 109.47^{\circ }} . The angles of the polyhedral structure are different; for instance, its edges meet at angles of 90

    Weaire–Phelan structure

    Weaire–Phelan structure

    Weaire–Phelan_structure

  • Conway polyhedron notation
  • Method of describing higher-order polyhedra

    equivalent polyhedra can be thought of as one of many embeddings of a polyhedral graph on the sphere. Unless otherwise specified, in this article (and

    Conway polyhedron notation

    Conway polyhedron notation

    Conway_polyhedron_notation

  • Cycle double cover
  • Cycles in a graph that cover each edge twice

    have repeating vertices, but not repeated edges. For instance, for any polyhedral graph, the faces of a convex polyhedron that represents the graph provide

    Cycle double cover

    Cycle double cover

    Cycle_double_cover

  • Staircase paradox
  • Curves whose limit does not preserve length

    dimensions, the Schwarz lantern provides an analogous example showing that polyhedral surfaces that converge pointwise to a curved surface do not necessarily

    Staircase paradox

    Staircase paradox

    Staircase_paradox

  • Jemmis mno rules
  • explain the structures of condensed polyhedral boranes such as B20H16, which are obtained by condensing polyhedral boranes by sharing a triangular face

    Jemmis mno rules

    Jemmis_mno_rules

  • Steinitz's theorem
  • Graph-theoretic description of polyhedra

    In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices

    Steinitz's theorem

    Steinitz's_theorem

  • Great complex icosidodecahedron
  • Degenerate uniform star polyhedron

    In geometry, the great complex icosidodecahedron is a degenerate uniform star polyhedron. It has 12 vertices, and 60 (doubled) edges, and 32 faces, 12

    Great complex icosidodecahedron

    Great complex icosidodecahedron

    Great_complex_icosidodecahedron

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

    stellation and may also be applied to higher-dimensional polytopes. In polyhedral combinatorics and in the general theory of polytopes, a face that has

    Facet (geometry)

    Facet_(geometry)

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

    include: Graph drawing Polyhedral graphs Random geometric graphs Voronoi diagrams and Delaunay triangulations A simplicial complex is a topological space

    Discrete geometry

    Discrete geometry

    Discrete_geometry

  • CAT(0) group
  • Type of group used in topology and geometric group theory

    André (1999), Bridson, Martin R.; Haefliger, André (eds.), "Mк-Polyhedral Complexes of Bounded Curvature", Metric Spaces of Non-Positive Curvature, Berlin

    CAT(0) group

    CAT(0)_group

  • Poincaré duality
  • Connects homology and cohomology groups for oriented closed manifolds

    cohomologies of the dual polyhedral/CW decomposition the manifold respectively. The fact that this is an isomorphism of chain complexes is a proof of Poincaré

    Poincaré duality

    Poincaré_duality

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

    figures by Stella4D software. Other convex 4-polytopes: Polyhedral pyramid Polyhedral bipyramid Polyhedral prism Infinite uniform 4-polytopes of Euclidean 3-space

    4-polytope

    4-polytope

    4-polytope

  • Polymake
  • Software for the algorithmic treatment of convex polyhedra

    polyhedra, it is by now also capable of dealing with simplicial complexes, matroids, polyhedral fans, graphs, tropical objects, toric varieties and other objects

    Polymake

    Polymake

    Polymake

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

    wedge defined by two non-parallel half-spaces, a polyhedral cylinder (infinite prism), and a polyhedral cone (infinite cone) defined by three or more half-spaces

    Convex polytope

    Convex polytope

    Convex_polytope

  • List of character tables for chemically important 3D point groups
  • order greater than 2. These polyhedral groups are characterized by not having a C5 proper rotation axis. These polyhedral groups are characterized by

    List of character tables for chemically important 3D point groups

    List_of_character_tables_for_chemically_important_3D_point_groups

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

    another problem on polyhedral nets, proved the Shephard–Todd theorem in invariant theory of finite groups, began the study of complex polytopes, and classified

    Geoffrey Colin Shephard

    Geoffrey_Colin_Shephard

  • Frank–Kasper phases
  • Particular class of intermetallic phases

    units, FK crystallographic structures are classified into low and high polyhedral groups denoted by their coordination numbers (CN) referring to the number

    Frank–Kasper phases

    Frank–Kasper phases

    Frank–Kasper_phases

  • Three-center two-electron bond
  • Electron-deficient chemical bond where three atoms share two electrons

    3c–2e bond model features heavily in cluster compounds described by the polyhedral skeletal electron pair theory, such as boranes and carboranes. These molecules

    Three-center two-electron bond

    Three-center_two-electron_bond

  • Johnson solid
  • Convex polyhedron with regular faces

    1007/978-94-017-1687-1. ISBN 978-94-017-1687-1. Diudea, M. V. (2018). Multi-shell Polyhedral Clusters. Carbon Materials: Chemistry and Physics. Vol. 10. Springer.

    Johnson solid

    Johnson_solid

  • Sandwich compound
  • Chemical compound made of two ring ligands bound to a metal

    carborane ligands to form polyhedral cages ranging in size from 6 to 15 vertices. Examples include bis(dicarbollide) complexes, such as [M(C2B9H11)2]z−

    Sandwich compound

    Sandwich compound

    Sandwich_compound

  • ADE classification
  • Mathematical classification

    subgroups of S U ( 2 ) {\displaystyle SU(2)} , the binary polyhedral groups; properly, binary polyhedral groups correspond to the simply laced affine Dynkin

    ADE classification

    ADE classification

    ADE_classification

  • The Ambassadors (Holbein)
  • 1533 painting by Hans Holbein

    and one celestial), a shepherd's dial, a quadrant, a torquetum, and a polyhedral sundial, as well as various textiles. The floor mosaic is based on a design

    The Ambassadors (Holbein)

    The Ambassadors (Holbein)

    The_Ambassadors_(Holbein)

  • Piecewise linear function
  • Type of mathematical function

    vector space, an affine space, a piecewise linear manifold, or a simplicial complex. (In these contexts, the term “linear” does not refer solely to linear

    Piecewise linear function

    Piecewise_linear_function

  • Earl Muetterties
  • American inorganic chemist

    polyhedral borane anions such as B12H122−. He was an inventor on some basic findings with the polyhedral borate anions. In addition to the polyhedral

    Earl Muetterties

    Earl Muetterties

    Earl_Muetterties

  • Grigori Perelman
  • Russian mathematician (born 1966)

    on the possibility of prescribing the structure of negatively-curved polyhedral surfaces in three-dimensional Euclidean space. He proved that any such

    Grigori Perelman

    Grigori Perelman

    Grigori_Perelman

  • Tissue (biology)
  • Group of similar cells performing a specific function

    tissue is present. Cells of this type of tissue are roughly spherical or polyhedral to rectangular in shape, with thin cell walls. New cells produced by meristem

    Tissue (biology)

    Tissue (biology)

    Tissue_(biology)

  • Siegel upper half-space
  • Space of complex matrices with positive definite imaginary part

    compactifications, which depend on the choice of an admissible rational polyhedral cone decomposition. For a projective admissible decomposition, the resulting

    Siegel upper half-space

    Siegel_upper_half-space

  • Bismuth(III) acetate
  • Chemical compound

    coordination complex with the formula Bi(O2CCH3)3. It is a molecular compound featuring Bi bound to six oxygen ligands in a distorted polyhedral sphere. According

    Bismuth(III) acetate

    Bismuth(III) acetate

    Bismuth(III)_acetate

  • Map projection
  • Systematic representation of the surface of a sphere or ellipsoid onto a plane

    locations closer than at a distance equal to the constant d0 are not shown. Polyhedral map projections use a polyhedron to subdivide the globe into faces, and

    Map projection

    Map projection

    Map_projection

  • Mercator projection
  • Cylindrical conformal map projection

    expressed using a single complex number to represent each point on the sphere rather than a pair of real-number coordinates. The complex number representing

    Mercator projection

    Mercator projection

    Mercator_projection

  • Combinatorial map
  • Combinatorial representation of a graph on an orientable surface

    concept of a combinatorial map was introduced informally by J. Edmonds for polyhedral surfaces which are planar graphs. It was given its first definite formal

    Combinatorial map

    Combinatorial_map

  • Real projective plane
  • Compact non-orientable two-dimensional manifold

    self-intersections) in 3-space. Boy's surface is an example of an immersion. Polyhedral examples must have at least nine faces. Steiner's Roman surface is a more

    Real projective plane

    Real projective plane

    Real_projective_plane

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

    all 4-polytopes is zero, we have the 4-dimensional analogue of Euler's polyhedral formula: N 0 − N 1 + N 2 − N 3 = 0 {\displaystyle N_{0}-N_{1}+N_{2}-N_{3}=0\

    Regular 4-polytope

    Regular 4-polytope

    Regular_4-polytope

  • Outline of geometry
  • Overview of and topical guide to geometry

    Archimedean solid Kepler-Poinsot polyhedra Johnson solid Uniform polyhedron Polyhedral compound Hilbert's third problem Deltahedron Surface normal 3-sphere,

    Outline of geometry

    Outline_of_geometry

  • Mathematical visualization
  • played an important role at the beginning of topological knot theory, when polyhedral decompositions were used to compute the homology of covering spaces of

    Mathematical visualization

    Mathematical visualization

    Mathematical_visualization

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

    vertices (0-faces), and the empty set. In some areas of mathematics, such as polyhedral combinatorics, a polytope is by definition convex. In this setting, there

    Face (geometry)

    Face (geometry)

    Face_(geometry)

  • Circle packing theorem
  • On tangency patterns of circles

    {\displaystyle G} . A stronger form of the circle packing theorem applies to any polyhedral graph and its dual graph, and proves the existence of a primal–dual packing

    Circle packing theorem

    Circle packing theorem

    Circle_packing_theorem

  • Orthogonal group
  • Type of group in mathematics

    Dimension 3 is particularly studied – see point groups in three dimensions, polyhedral groups, and list of spherical symmetry groups. In 2 dimensions, the finite

    Orthogonal group

    Orthogonal group

    Orthogonal_group

  • Combinatorial commutative algebra
  • Field of mathematics using techniques from combinatorics and commutative algebra

    methods of one to address problems arising in the other. Less obviously, polyhedral geometry plays a significant role. One of the milestones in the development

    Combinatorial commutative algebra

    Combinatorial_commutative_algebra

  • K3 surface
  • Type of smooth complex surface of kodaira dimension 0

    Hans Sterk, is that Aut(X) acts on the nef cone of X with a rational polyhedral fundamental domain. K3 surfaces appear almost ubiquitously in string duality

    K3 surface

    K3 surface

    K3_surface

  • OLED
  • Diode that emits light from an organic compound

    coordinates (for white emission). The use of macromolecular species like polyhedral oligomeric silsesquioxanes (POSS) in conjunction with the use of phosphorescent

    OLED

    OLED

    OLED

  • Möbius transformation
  • Rational function of the form (az + b)/(cz + d)

    this maximal compact group, and thus these correspond exactly to the polyhedral groups, the point groups in three dimensions. Icosahedral groups of Möbius

    Möbius transformation

    Möbius_transformation

  • MLIR (software)
  • C++ framework for compiler development

    dialects such as affine, which supports affine loop nests suitable for polyhedral optimization, and scf, which provides structured control flow using constructs

    MLIR (software)

    MLIR (software)

    MLIR_(software)

  • Computer vision
  • Computerized information extraction from images

    including extraction of edges from images, labeling of lines, non-polyhedral and polyhedral modeling, representation of objects as interconnections of smaller

    Computer vision

    Computer_vision

  • Mathematics and art
  • was a German Renaissance printmaker who made important contributions to polyhedral literature in his 1525 book, Underweysung der Messung (Education on Measurement)

    Mathematics and art

    Mathematics and art

    Mathematics_and_art

  • Graph theory
  • Area of discrete mathematics

    diagonals of a polygon. The vertices are defined as the point locations. Polyhedral graph is an undirected graph that forms the vertices and edges of a three-dimensional

    Graph theory

    Graph theory

    Graph_theory

  • Polygon mesh
  • Set of polygons to define the surface of a 3D model

    a collection of vertices, edges and faces that define the shape of a polyhedral object's surface. It simplifies rendering, as in a wire-frame model. The

    Polygon mesh

    Polygon mesh

    Polygon_mesh

  • Bipyramid
  • Polyhedron formed by joining mirroring pyramids base-to-base

    B. C.; Sülzle, D.; Hauer, H. "Onion-Like Inorganic Fullerenes from a Polyhedral Perspective". In Sattler, Klaus D. (ed.). 21st Century Nanoscience: A

    Bipyramid

    Bipyramid

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

    complementary chord pairs corresponds to a distinct pair of opposing polyhedral sections of the 120-cell, beginning with a vertex, the 00 section. The

    120-cell

    120-cell

    120-cell

  • List of unsolved problems in mathematics
  • with planar covers The strong Papadimitriou–Ratajczak conjecture: every polyhedral graph has a convex greedy embedding Turán's brick factory problem – Is

    List of unsolved problems in mathematics

    List_of_unsolved_problems_in_mathematics

  • Mathieu group M24
  • Sporadic simple group

    topologically but not geometrically the t0,1{4, 3, 3} tiling, and can be (polyhedrally) immersed in Euclidean 3-space as the small cubicuboctahedron (which

    Mathieu group M24

    Mathieu group M24

    Mathieu_group_M24

  • Brateiu Archaeological Complex
  • Archaeological site in Transylvania, Romania

    gold and silver earrings, fibulae, buckles, and gold pins with openwork polyhedral heads. An interesting detail is that a specific type of necklace regularly

    Brateiu Archaeological Complex

    Brateiu_Archaeological_Complex

  • Buckminsterfullerene
  • Cage-like allotrope of carbon

    candidates for the carrier of the diffuse interstellar bands: C+ 60 and other polyhedral carbon ions". Astron. Astrophys. 203 (1): 145. Bibcode:1988A&A...203.

    Buckminsterfullerene

    Buckminsterfullerene

    Buckminsterfullerene

  • Organoboron chemistry
  • Study of compounds containing a boron-carbon bond

    species. Organometallic compounds with metal-boron bonds (M–BR2) are boryl complexes, corresponding to the notional boryl anion R2B−, although the latter cannot

    Organoboron chemistry

    Organoboron chemistry

    Organoboron_chemistry

  • Roald Hoffmann
  • Nobel laureate theoretical chemist

    William N. Lipscomb Jr. Hoffman worked on the molecular orbital theory of polyhedral molecules. Under Lipscomb's direction the Extended Hückel method was developed

    Roald Hoffmann

    Roald Hoffmann

    Roald_Hoffmann

  • Cubic surface
  • Algebraic surface defined by a cubic polynomial

    field is the complex numbers). For a cubic surface, the cone of curves is spanned by the 27 lines. In particular, it is a rational polyhedral cone in N 1

    Cubic surface

    Cubic surface

    Cubic_surface

  • Fullerene
  • Allotrope of carbon

    known with ellipsoid-like shapes. Fullerenes have also been described as "polyhedral closed cages made up entirely of n three-coordinate carbon atoms and having

    Fullerene

    Fullerene

    Fullerene

  • Clathrate compound
  • Chemical substance consisting of a cage-like host lattice containing guest species

    elements such as silicon, germanium, or tin, that enclose guest atoms in polyhedral cages. The properties of a clathrate depend on both the host framework

    Clathrate compound

    Clathrate_compound

  • Glossary of areas of mathematics
  • frequently employs methods from one to address problems arising in the other. Polyhedral geometry also plays a significant role. Combinatorial design theory a

    Glossary of areas of mathematics

    Glossary_of_areas_of_mathematics

  • Glossary of mathematical symbols
  • Physical constants Notational systems in geometry: Christoffel symbols Polyhedral symbol Schläfli symbol Geometric dimensioning and tolerancing Well-known

    Glossary of mathematical symbols

    Glossary_of_mathematical_symbols

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POLYHEDRAL COMPLEX

  • Polyhedra
  • pl.

    of Polyhedron

  • Complexness
  • n.

    The state of being complex; complexity.

  • Complexity
  • n.

    The state of being complex; intricacy; entanglement.

  • Holohedral
  • a.

    Having all the planes required by complete symmetry, -- in opposition to hemihedral.

  • Complexity
  • n.

    That which is complex; intricacy; complication.

  • Polyhedrous
  • a.

    Polyhedral.

  • Anamorphosis
  • n.

    A distorted or monstrous projection or representation of an image on a plane or curved surface, which, when viewed from a certain point, or as reflected from a curved mirror or through a polyhedron, appears regular and in proportion; a deformation of an image.

  • Polyacron
  • n.

    A solid having many summits or angular points; a polyhedron.

  • Complexionary
  • a.

    Pertaining to the complexion, or to the care of it.

  • Polyhedron
  • n.

    A polyscope, or multiplying glass.

  • Polyhedral
  • a.

    Alt. of Polyhedrical

  • Polyedrous
  • a.

    See Polyhedral.

  • Complexus
  • n.

    A complex; an aggregate of parts; a complication.

  • Polyhedron
  • n.

    A body or solid contained by many sides or planes.

  • Polyhedrons
  • pl.

    of Polyhedron

  • Complexioned
  • a.

    Having (such) a complexion; -- used in composition; as, a dark-complexioned or a ruddy-complexioned person.

  • Polyhedrical
  • a.

    Having many sides, as a solid body.

  • Complexities
  • pl.

    of Complexity

  • Polyedron
  • n.

    See Polyhedron.

  • Complexly
  • adv.

    In a complex manner; not simply.