HOME  TheInfoList.com 
Vertex Figure In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.Contents1 Definitions1.1 As a flat slice 1.2 As a spherical polygon 1.3 As the set of connected vertices 1.4 Abstract definition2 General properties 3 Constructions3.1 From the adjacent vertices 3.2 Dorman Luke Dorman Luke construction 3.3 Regular polytopes4 An example vertex figure of a honeycomb 5 Edge figure 6 See also 7 References7.1 Notes 7.2 Bibliography8 External linksDefinitions[edit]"Wholeedge" vertex figure of the cubeSpherical vertex figure of the cubePointset vertex figure of the cubeTake some corner or vertex of a polyhedron. Mark a point somewhere along each connected edge. Draw lines across the connected faces, joining adjacent points around the face. When done, these lines form a complete circuit, i.e. a polygon, around the vertex [...More...]  "Vertex Figure" on: Wikipedia Yahoo 

Geometry Geometry Geometry (from the Ancient Greek: γεωμετρία; geo "earth", metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes [...More...]  "Geometry" on: Wikipedia Yahoo 

Special Special Special or specials may refer to:Contents1 Music 2 Film and television 3 Other uses 4 See alsoMusic[edit] Special Special (album), a 1992 album by Vesta Williams "Special" (Garbage song), 1998 "Special [...More...]  "Special" on: Wikipedia Yahoo 

Facet (geometry) In geometry, a facet is a feature of a polyhedron, polytope, or related geometric structure, generally of dimension one less than the structure itself.In threedimensional geometry a facet of a polyhedron is any polygon whose corners are vertices of the polyhedron, and is not a face.[1][2] To facet a polyhedron is to find and join such facets to form the faces of a new polyhedron; this is the reciprocal process to stellation and may also be applied to higherdimensional polytopes.[3] In polyhedral combinatorics and in the general theory of polytopes, a facet of a polytope of dimension n is a face that has dimension n − 1. Facets may also be called (n − 1)faces [...More...]  "Facet (geometry)" on: Wikipedia Yahoo 

Graph Theory In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices, nodes, or points which are connected by edges, arcs, or lines. A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another; see Graph (discrete mathematics) Graph (discrete mathematics) for more detailed definitions and for other variations in the types of graph that are commonly considered [...More...]  "Graph Theory" on: Wikipedia Yahoo 

Star Polygon In geometry, a star polygon is a type of nonconvex polygon. Only the regular star polygons have been studied in any depth; star polygons in general appear not to have been formally defined. Branko Grünbaum Branko Grünbaum identified two primary definitions used by Kepler, one being the regular star polygons with intersecting edges that don't generate new vertices, and the second being simple isotoxal concave polygons.[1] The first usage is included in polygrams which includes polygons like the pentagram but also compound figures like the hexagram.Contents1 Etymology 2 Regular star polygon2.1 Degenerate regular star polygons3 Simple isotoxal star polygons 4 Interiors of star polygons 5 Star polygons in art and culture 6 See also 7 ReferencesEtymology[edit] Star polygon Star polygon names combine a numeral prefix, such as penta, with the Greek suffix gram (in this case generating the word pentagram) [...More...]  "Star Polygon" on: Wikipedia Yahoo 

Hyperplane In geometry a hyperplane is a subspace whose dimension is one less than that of its ambient space. If a space is 3dimensional then its hyperplanes are the 2dimensional planes, while if the space is 2dimensional, its hyperplanes are the 1dimensional lines. This notion can be used in any general space in which the concept of the dimension of a subspace is defined. In different settings, the objects which are hyperplanes may have different properties. For instance, a hyperplane of an ndimensional affine space is a flat subset with dimension n − 1. By its nature, it separates the space into two half spaces [...More...]  "Hyperplane" on: Wikipedia Yahoo 

Coxeter Diagram In geometry, a Coxeter– Dynkin diagram Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing the spatial relations between a collection of mirrors (or reflecting hyperplanes). It describes a kaleidoscopic construction: each graph "node" represents a mirror (domain facet) and the label attached to a branch encodes the dihedral angle order between two mirrors (on a domain ridge). An unlabeled branch implicitly represents order3. Each diagram represents a Coxeter group, and Coxeter groups are classified by their associated diagrams. Dynkin diagrams are closely related objects, which differ from Coxeter diagrams in two respects: firstly, branches labeled "4" or greater are directed, while Coxeter diagrams are undirected; secondly, Dynkin diagrams must satisfy an additional (crystallographic) restriction, namely that the only allowed branch labels are 2, 3, 4, and 6 [...More...]  "Coxeter Diagram" on: Wikipedia Yahoo 

Harold Scott MacDonald Coxeter Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, CC (February 9, 1907 – March 31, 2003)[2] was a Britishborn Canadian geometer. Coxeter is regarded as one of the greatest geometers of the 20th century. He was born in London London but spent most of his adult life in Canada. He was always called Donald, from his third name MacDonald.[3] He was most noted for his work on regular polytopes and higherdimensional geometries [...More...]  "Harold Scott MacDonald Coxeter" on: Wikipedia Yahoo 

Square Pyramid In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it will have C4v symmetry.Contents1 Johnson solid Johnson solid (J1) 2 Other square pyramids 3 Related polyhedra and honeycombs3.1 Dual polyhedron4 Topology 5 Examples 6 References 7 External links Johnson solid Johnson solid (J1)[edit] If the sides are all equilateral triangles, the pyramid is one of the Johnson solids (J1). The 92 Johnson solids were named and described by Norman Johnson in 1966. A Johnson solid Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms, or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.[1] The Johnson square pyramid can be characterized by a single edgelength parameter a [...More...]  "Square Pyramid" on: Wikipedia Yahoo 

International Standard Book Number "ISBN" redirects here. For other uses, see ISBN (other).International Standard Book Book NumberA 13digit ISBN, 9783161484100, as represented by an EAN13 bar codeAcronym ISBNIntroduced 1970; 48 years ago (1970)Managing organisation International ISBN AgencyNo. of digits 13 (formerly 10)Check digit Weighted sumExample 9783161484100Website www.isbninternational.orgThe International Standard Book Book Number (ISBN) is a unique[a][b] numeric commercial book identifier. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.[1] An ISBN is assigned to each edition and variation (except reprintings) of a book. For example, an ebook, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, and 10 digits long if assigned before 2007 [...More...]  "International Standard Book Number" on: Wikipedia Yahoo 

Isogonal Figure In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertextransitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of face in the same or reverse order, and with the same angles between corresponding faces. Technically, we say that for any two vertices there exists a symmetry of the polytope mapping the first isometrically onto the second. Other ways of saying this are that the group of automorphisms of the polytope is transitive on its vertices, or that the vertices lie within a single symmetry orbit. All vertices of a finite ndimensional isogonal figure exist on an (n1)sphere.[citation needed] The term isogonal has long been used for polyhedra [...More...]  "Isogonal Figure" on: Wikipedia Yahoo 

Polygon In elementary geometry, a polygon (/ˈpɒlɪɡɒn/) is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit. These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or corners. The interior of the polygon is sometimes called its body. An ngon is a polygon with n sides; for example, a triangle is a 3gon. A polygon is a 2dimensional example of the more general polytope in any number of dimensions. The basic geometrical notion of a polygon has been adapted in various ways to suit particular purposes. Mathematicians are often concerned only with the bounding closed polygonal chain and with simple polygons which do not selfintersect, and they often define a polygon accordingly. A polygonal boundary may be allowed to intersect itself, creating star polygons and other selfintersecting polygons [...More...]  "Polygon" on: Wikipedia Yahoo 

Eric W. Weisstein Eric Wolfgang Weisstein (born March 18, 1969) is an encyclopedist who created and maintains MathWorld and Eric Weisstein's World of Science (ScienceWorld). He is the author of the CRC Concise Encyclopedia of Mathematics. He currently works for Wolfram Research, Inc.Contents1 Education 2 Career2.1 Academic research 2.2 MathWorld, ScienceWorld ScienceWorld and Wolfram Research 2.3 Further scientific activities3 Footnotes 4 References 5 External linksEducation[edit] Weisstein holds a Ph.D. in planetary astronomy which he obtained from the California Institute of Technology's (Caltech) Division of Geological and Planetary Sciences in 1996 as well as an M.S. in planetary astronomy in 1993 also from Caltech. Weisstein graduated Cum Laude from Cornell University Cornell University with a B.A. in physics and a minor in astronomy in 1990 [...More...]  "Eric W. Weisstein" on: Wikipedia Yahoo 

Convex Polytope A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the ndimensional space Rn.[1] Some authors use the terms "convex polytope" and "convex polyhedron" interchangeably, while others prefer to draw a distinction between the notions of a polyhedron and a polytope. In addition, some texts require a polytope to be a bounded set, while others[2] (including this article) allow polytopes to be unbounded. The terms "bounded/unbounded convex polytope" will be used below whenever the boundedness is critical to the discussed issue. Yet other texts treat a convex npolytope as a surface or (n1)manifold. Convex polytopes play an important role both in various branches of mathematics and in applied areas, most notably in linear programming. A comprehensive and influential book in the subject, called Convex Polytopes, was published in 1967 by Branko Grünbaum [...More...]  "Convex Polytope" on: Wikipedia Yahoo 