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Uniform 9-polytope
In nine-dimensional geometry, a nine-dimensional polytope or 9-polytope is a polytope contained by 8-polytope facets. Each 7-polytope ridge being shared by exactly two 8-polytope facets. A uniform 9-polytope is one which is vertex-transitive, and constructed from uniform 8-polytope Facet (geometry), facets. Regular 9-polytopes Regular 9-polytopes can be represented by the Schläfli symbol , with w 8-polytope facets A facet is a flat surface of a geometric shape, e.g., of a cut gemstone. Facet may also refer to: Arts, entertainment, and media * ''Facets'' (album), an album by Jim Croce * ''Facets'', a 1980 album by jazz pianist Monty Alexander and his tri ... around each Peak (geometry), peak. There are exactly three such List of regular polytopes#Convex 4, convex regular 9-polytopes: # - 9-simplex # - 9-cube # - 9-orthoplex There are no nonconvex regular 9-polytopes. Euler characteristic The topology of any given 9-polytope is defined by its Betti numbers and tor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Regular Polytopes
This article lists the regular polytopes and regular polytope compounds in Euclidean geometry, Euclidean, spherical geometry, spherical and hyperbolic geometry, hyperbolic spaces. The Schläfli symbol describes every regular tessellation of an ''n''-sphere, Euclidean and hyperbolic spaces. A Schläfli symbol describing an ''n''-polytope equivalently describes a tessellation of an (''n'' − 1)-sphere. In addition, the symmetry of a regular polytope or tessellation is expressed as a Coxeter group, which Coxeter expressed identically to the Schläfli symbol, except delimiting by square brackets, a notation that is called Coxeter notation. Another related symbol is the Coxeter-Dynkin diagram which represents a symmetry group with no rings, and the represents regular polytope or tessellation with a ring on the first node. For example, the cube has Schläfli symbol , and with its octahedral symmetry, [4,3] or , it is represented by Coxeter diagram . The regular polytopes are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncated 9-demicube
Truncation is the term used for limiting the number of digits right of the decimal point by discarding the least significant ones. Truncation may also refer to: Mathematics * Truncation (statistics) refers to measurements which have been cut off at some value * Truncation (numerical analysis) refers to truncating an infinite sum by a finite one * Truncation (geometry) is the removal of one or more parts, as for example in truncated cube * Propositional truncation, a type former which truncates a type down to a mere proposition Computer science * Data truncation, an event that occurs when a file or other data is stored in a location too small to accommodate its entire length * Truncate (SQL), a command in the SQL data manipulation language to quickly remove all data from a table Biology * Truncate, a leaf shape * Truncated protein, a protein shortened by a mutation which specifically induces premature termination of messenger RNA translation Other uses * Cheque truncation, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
9-demicube
In geometry, a demienneract or 9-demicube is a uniform 9-polytope, constructed from the 9-cube, with alternated vertices removed. It is part of a dimensionally infinite family of uniform polytopes called demihypercubes. E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as HM9 for a 9-dimensional ''half measure'' polytope. Coxeter named this polytope as 161 from its Coxeter diagram, with a ring on one of the 1-length branches, and Schläfli symbol \left\ or . Cartesian coordinates Cartesian coordinates for the vertices of a demienneract centered at the origin are alternate halves of the enneract: : (±1,±1,±1,±1,±1,±1,±1,±1,±1) with an odd number of plus signs. Images References * H.S.M. Coxeter: ** Coxeter, ''Regular Polytopes'', (3rd edition, 1973), Dover edition, , p. 296, Table I (iii): Regular Polytopes, three regular polytopes in n-dimensions (n≥5) ** H.S.M. Coxeter, ''Regular Polytopes'', 3rd Edition, Dover New York, 1973, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectified 9-cube
In nine-dimensional geometry, a rectified 9-cube is a convex uniform 9-polytope, being a rectification of the regular 9-cube. There are 9 rectifications of the 9-cube. The zeroth is the 9-cube itself, and the 8th is the dual 9-orthoplex. Vertices of the rectified 9-cube are located at the edge-centers of the 9-orthoplex. Vertices of the birectified 9-cube are located in the square face centers of the 9-cube. Vertices of the trirectified 9-orthoplex are located in the cube cell centers of the 9-cube. Vertices of the quadrirectified 9-cube are located in the tesseract centers of the 9-cube. These polytopes are part of a family 511 uniform 9-polytope In nine-dimensional geometry, a nine-dimensional polytope or 9-polytope is a polytope contained by 8-polytope facets. Each 7-polytope ridge being shared by exactly two 8-polytope facets. A uniform 9-polytope is one which is vertex-transitive, and ...s with BC9 symmetry. Rectified 9-cube Alternate names * Rectified enneract (Acronym ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectified 9-orthoplex
In nine-dimensional geometry, a rectified 9-simplex is a convex uniform 9-polytope, being a rectification of the regular 9-orthoplex. There are 9 rectifications of the 9-orthoplex. Vertices of the rectified 9-orthoplex are located at the edge-centers of the 9-orthoplex. Vertices of the birectified 9-orthoplex are located in the triangular face centers of the 9-orthoplex. Vertices of the trirectified 9-orthoplex are located in the tetrahedral cell centers of the 9-orthoplex. These polytopes are part of a family 511 uniform 9-polytopes with BC9 symmetry. Rectified 9-orthoplex The ''rectified 9-orthoplex'' is the vertex figure for the demienneractic honeycomb. : or Alternate names * rectified enneacross (Acronym riv) (Jonathan Bowers) Construction There are two Coxeter groups associated with the ''rectified 9-orthoplex'', one with the C9 or ,37Coxeter group, and a lower symmetry with two copies of 8-orthoplex facets, alternating, with the D9 or 6,1,1Coxeter group. C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectified Enneacross
In nine-dimensional geometry, a rectified 9-simplex is a convex uniform 9-polytope, being a rectification of the regular 9-orthoplex. There are 9 rectifications of the 9-orthoplex. Vertices of the rectified 9-orthoplex are located at the edge-centers of the 9-orthoplex. Vertices of the birectified 9-orthoplex are located in the triangular face centers of the 9-orthoplex. Vertices of the trirectified 9-orthoplex are located in the tetrahedral cell centers of the 9-orthoplex. These polytopes are part of a family 511 uniform 9-polytopes with BC9 symmetry. Rectified 9-orthoplex The ''rectified 9-orthoplex'' is the vertex figure for the demienneractic honeycomb. : or Alternate names * rectified enneacross (Acronym riv) (Jonathan Bowers) Construction There are two Coxeter groups associated with the ''rectified 9-orthoplex'', one with the C9 or ,37Coxeter group, and a lower symmetry with two copies of 8-orthoplex facets, alternating, with the D9 or 6,1,1Coxeter group. C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncated 9-cube
Truncation is the term used for limiting the number of digits right of the decimal point by discarding the least significant ones. Truncation may also refer to: Mathematics * Truncation (statistics) refers to measurements which have been cut off at some value * Truncation (numerical analysis) refers to truncating an infinite sum by a finite one * Truncation (geometry) is the removal of one or more parts, as for example in truncated cube * Propositional truncation, a type former which truncates a type down to a mere proposition Computer science * Data truncation, an event that occurs when a file or other data is stored in a location too small to accommodate its entire length * Truncate (SQL), a command in the SQL data manipulation language to quickly remove all data from a table Biology * Truncate, a leaf shape * Truncated protein, a protein shortened by a mutation which specifically induces premature termination of messenger RNA translation Other uses * Cheque truncation, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truncated 9-orthoplex
Truncation is the term used for limiting the number of digits right of the decimal point by discarding the least significant ones. Truncation may also refer to: Mathematics * Truncation (statistics) refers to measurements which have been cut off at some value * Truncation (numerical analysis) refers to truncating an infinite sum by a finite one * Truncation (geometry) is the removal of one or more parts, as for example in truncated cube * Propositional truncation, a type former which truncates a type down to a mere proposition Computer science * Data truncation, an event that occurs when a file or other data is stored in a location too small to accommodate its entire length * Truncate (SQL), a command in the SQL data manipulation language to quickly remove all data from a table Biology * Truncate, a leaf shape * Truncated protein, a protein shortened by a mutation which specifically induces premature termination of messenger RNA translation Other uses * Cheque truncation, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
9-cube
In geometry, a 9-cube is a nine-dimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4-faces, 2016 5-cube 5-faces, 672 6-cube 6-faces, 144 7-cube 7-faces, and 18 8-cube 8-faces. It can be named by its Schläfli symbol , being composed of three 8-cubes around each 7-face. It is also called an enneract, a portmanteau of tesseract (the ''4-cube'') and ''enne'' for nine (dimensions) in Greek. It can also be called a regular octadeca-9-tope or octadecayotton, as a nine-dimensional polytope constructed with 18 regular facets. It is a part of an infinite family of polytopes, called hypercubes. The dual of a 9-cube can be called a 9-orthoplex, and is a part of the infinite family of cross-polytopes. Cartesian coordinates Cartesian coordinates for the vertices of a 9-cube centered at the origin and edge length 2 are : (±1,±1,±1,±1,±1,±1,±1,±1,±1) while the interior of the same consists of all points (''x''0, ''x''1, '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
9-orthoplex
In geometry, a 9-orthoplex or 9-cross polytope, is a regular 9-polytope with 18 vertices, 144 edges, 672 triangle faces, 2016 tetrahedron cells, 4032 5-cells ''4-faces'', 5376 5-simplex ''5-faces'', 4608 6-simplex ''6-faces'', 2304 7-simplex ''7-faces'', and 512 8-simplex ''8-faces''. It has two constructed forms, the first being regular with Schläfli symbol , and the second with alternately labeled (checkerboarded) facets, with Schläfli symbol or Coxeter symbol 611. It is one of an infinite family of polytopes, called cross-polytopes or ''orthoplexes''. The dual polytope is the 9-hypercube or enneract. Alternate names * Enneacross, derived from combining the family name ''cross polytope'' with ''ennea'' for nine (dimensions) in Greek language, Greek * Pentacosidodecayotton as a 512-Facet (geometry), facetted 9-polytope (polyyotton) Construction There are two Coxeter groups associated with the 9-orthoplex, one regular polytope, regular, Dual polytope, dual of the enner ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
