HOME  TheInfoList.com 
6simplex f5 = 7, f4 = 21, C = 35, F = 35, E = 21, V = 7 (χ=0)Coxeter group A6, [35], order 5040Bowers name and (acronym) Heptapeton (hop)Vertex figure 5simplexCircumradius 0.645497Properties convex, isogonal selfdualIn geometry, a 6simplex 6simplex is a selfdual regular 6polytope. It has 7 vertices, 21 edges, 35 triangle faces, 35 tetrahedral cells, 21 5cell 4faces, and 7 5simplex 5simplex 5faces. Its dihedral angle is cos−1(1/6), or approximately 80.41°.Contents1 Alternate names 2 As a configuration 3 Coordinates 4 Images 5 Related uniform 6polytopes 6 Notes 7 References 8 External linksAlternate names[edit] It can also be called a heptapeton, or hepta6tope, as a 7facetted polytope in 6dimensions. The name heptapeton is derived from hepta for seven facets in Greek and peta for having fivedimensional facets, and on [...More...]  "6simplex" on: Wikipedia Yahoo Parouse 

Peta Peta /ˈpɛ.tə/ is a decimal unit prefix in the metric system denoting multiplication by 1015 (1000000000000000). It was adopted as an SI prefix SI prefix in the International System of Units International System of Units in 1975,[1] and has the symbol P. Peta is derived from the Greek πέντε, meaning "five". It denotes the fifth power of 1000 (10005). It is similar to the prefix penta ("five"), but without the letter n (on the analogy of the prefix tera (from the Greek for "monster") for 10004 looking like tetra ("four") with a letter missing). Examples:1 petametre = 1015 metres 1 petasecond = 1015 seconds (31.7 million years) 1 petahertz = 1015 cycle per second [...More...]  "Peta" on: Wikipedia Yahoo Parouse 

Vertex (geometry) In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet [...More...]  "Vertex (geometry)" on: Wikipedia Yahoo Parouse 

Orthographic Projection Orthographic projection Orthographic projection (sometimes orthogonal projection), is a means of representing threedimensional objects in two dimensions. It is a form of parallel projection, in which all the projection lines are orthogonal to the projection plane,[1] resulting in every plane of the scene appearing in affine transformation on the viewing surface. The obverse of an orthographic projection is an oblique projection, which is a parallel projection in which the projection lines are not orthogonal to the projection plane. The term orthographic is sometimes reserved specifically for depictions of objects where the principal axes or planes of the object are also parallel with the projection plane,[1] but these are better known as multiview projections [...More...]  "Orthographic Projection" on: Wikipedia Yahoo Parouse 

Cartesian Coordinate A Cartesian coordinate system Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis (plural axes) of the system, and the point where they meet is its origin, at ordered pair (0, 0) [...More...]  "Cartesian Coordinate" on: Wikipedia Yahoo Parouse 

Fvector Polyhedral combinatorics Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higherdimensional convex polytopes. Research in polyhedral combinatorics falls into two distinct areas. Mathematicians in this area study the combinatorics of polytopes; for instance, they seek inequalities that describe the relations between the numbers of vertices, edges, and faces of higher dimensions in arbitrary polytopes or in certain important subclasses of polytopes, and study other combinatorial properties of polytopes such as their connectivity and diameter (number of steps needed to reach any vertex from any other vertex) [...More...]  "Fvector" on: Wikipedia Yahoo Parouse 

Configuration (polytope) In geometry, H. S. M. Coxeter H. S. M. Coxeter called a regular polytope a special kind of configuration. Other configurations in geometry are something different. These polytope configurations may more accurately called incidence matrices, where like elements are collected together in rows and columns. Regular polytopes will have one row and column per kface element, while other polytopes will have one row and column for each kface type by their symmetry classes. A polytope with no symmetry will have one row and column for every element, and the matrix will be filled with 0 if the elements are not connected, and 1 if they are connected. Elements of the same k will not be connected and will have a "*" table entry [...More...]  "Configuration (polytope)" on: Wikipedia Yahoo Parouse 

Schläfli Symbol In geometry, the Schläfli symbol Schläfli symbol is a notation of the form p,q,r,... that defines regular polytopes and tessellations. The Schläfli symbol Schläfli symbol is named after the 19thcen [...More...]  "Schläfli Symbol" on: Wikipedia Yahoo Parouse 

Greek Language Greek (Modern Greek: ελληνικά [eliniˈka], elliniká, "Greek", ελληνική γλώσσα [eliniˈci ˈɣlosa] ( listen), ellinikí glóssa, "Greek language") is an independent branch of the IndoEuropean family of languages, native to Greece Greece and other parts of the Eastern Mediterranean [...More...]  "Greek Language" on: Wikipedia Yahoo Parouse 

Facet (mathematics) 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 (mathematics)" on: Wikipedia Yahoo Parouse 

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 Parouse 

Dihedral Angle A dihedral angle is the angle between two intersecting planes. In chemistry it is the angle between planes through two sets of three atoms, having two atoms in common. In solid geometry it is defined as the union of a line and two halfplanes that have this line as a common edge [...More...]  "Dihedral Angle" on: Wikipedia Yahoo Parouse 

Cell (mathematics) In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object;[1] a threedimensional solid bounded exclusively by flat faces is a polyhedron. In more technical treatments of the geometry of polyhedra and higherdimensional polytopes, the term is also used to mean an element of any dimension of a more general polytope (in any number of dimensions).[2]Contents1 Polygonal face1.1 Number of polygonal faces of a polyhedron2 kface2.1 Cell or 3face 2.2 Facet or (n1)face 2.3 Ridge or (n2)face 2.4 Peak or (n3)face3 See also 4 References 5 External linksPolygonal face[edit] In elementary geometry, a face is a polygon on the boundary of a polyhedron.[2][3] Other names for a polygonal face include side of a polyhedron, and tile of a Euclidean plane tessellation. For example, any of the six squares that bound a cube is a face of the cube. Sometimes "face" is also used to refer to the 2dimensional features of a 4polytope [...More...]  "Cell (mathematics)" on: Wikipedia Yahoo Parouse 

Face (geometry) In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object;[1] a threedimensional solid bounded exclusively by flat faces is a polyhedron. In more technical treatments of the geometry of polyhedra and higherdimensional polytopes, the term is also used to mean an element of any dimension of a more general polytope (in any number of dimensions).[2]Contents1 Polygonal face1.1 Number of polygonal faces of a polyhedron2 kface2.1 Cell or 3face 2.2 Facet or (n1)face 2.3 Ridge or (n2)face 2.4 Peak or (n3)face3 See also 4 References 5 External linksPolygonal face[edit] In elementary geometry, a face is a polygon on the boundary of a polyhedron.[2][3] Other names for a polygonal face include side of a polyhedron, and tile of a Euclidean plane tessellation. For example, any of the six squares that bound a cube is a face of the cube. Sometimes "face" is also used to refer to the 2dimensional features of a 4polytope [...More...]  "Face (geometry)" on: Wikipedia Yahoo Parouse 

Dihedral Symmetry In mathematics, a dihedral group is the group of symmetries of a regular polygon,[1][2] which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry. The notation for the dihedral group differs in geometry and abstract algebra. In geometry, Dn or Dihn refers to the symmetries of the ngon, a group of order 2n [...More...]  "Dihedral Symmetry" on: Wikipedia Yahoo Parouse 

Edge (geometry) In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higherdimensional polytope.[1] In a polygon, an edge is a line segment on the boundary,[2] and is often called a side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces meet.[3] A segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal.Contents1 Relation to edges in graphs 2 Number of edges in a polyhedron 3 Incidences with other faces 4 Alternative terminology 5 See also 6 References 7 External linksRelation to edges in graphs[edit] In graph theory, an edge is an abstract object connecting two graph vertices, unlike polygon and polyhedron edges which have a concrete geometric representation as a line segment [...More...]  "Edge (geometry)" on: Wikipedia Yahoo Parouse 