Uniform polypeton db Uniform polypeton stat table hop In geometry , a 6 simplex is a Duality mathematics self dual Regular polytope regular 6 polytope . It has 7 vertex geometry vertices , 21 Edge geometry edge s, 35 triangle Face geometry faces , 35 Tetrahedron tetrahedral Cell mathematics cells , 21 5 cell 4 faces, and 7 5 simplex 5 faces. Its dihedral angle is cos sup 1 sup 1 6 , or approximately 80.41 . Alternate names It can also be called a heptapeton , or hepta 6 tope , as a 7 facet geometry facetted polytope in 6 dimensions. The 5 polytope A note on generality of terms for n polytopes and elements name heptapeton is derived from hepta for seven Facet mathematics facets in Greek language Greek and Peta peta for having five dimensional facets, and on . Jonathan Bowers gives a heptapeton the acronym hop . ref Klitzing, x3o3o3o3o3o hop ref Coordinates The Cartesian coordinate s for an origin centered regular heptapeton having edge length 2 are math left sqrt 1 21 , sqrt 1 15 , sqrt 1 10 , sqrt 1 6 , sqrt 1 3 , pm1 right math math left sqrt 1 21 , sqrt 1 15 , sqrt 1 10 , sqrt 1 6 , 2 sqrt 1 3 , 0 right math math left sqrt 1 21 , sqrt 1 15 , sqrt 1 10 , sqrt 3 2 , 0, 0 right math math left sqrt 1 21 , sqrt 1 15 , 2 sqrt 2 5 , 0, 0, 0 right math math left sqrt 1 21 , sqrt 5 3 , 0, 0, 0, 0 right math math left sqrt 12 7 , 0, 0, 0, 0, 0 right math The vertices of the 6 simplex can be more simply positioned in 7 space as permutations of 0,0,0,0,0,0,1 This construction is based on Facet geometry facets of the 7 orthoplex . Images 6 simplex Coxeter plane graphs t0 150 Related uniform 6 polytopes The regular 6 simplex is one of 35 Uniform 6 polytope The A6 .5B3.2C3.2C3.2C3.2C3.5D family .286 simplex.29 uniform 6 polytopes based on the 3,3,3,3,3 Coxeter group , all shown here in A sub 6 sub Coxeter plane orthographic projection s. Heptapeton family Notes reflist References Harold Scott MacDonald Coxeter H.S.M. Coxeter Coxeter, Regular Polytopes book Regular Polytopes ... more details
Alternate names Small rhombated heptapeton Acronym sril Jonathan Bowers ref Klitizing, x3o3x3o3o3o sril ... Convex polytope convex Alternate names Small prismated heptapeton Acronym sabril Jonathan Bowers ref ... polytope convex Alternate names Great rhombated heptapeton Acronym gril Jonathan Bowers ref Klitzing ... Convex polytope convex Alternate names Great birhombated heptapeton Acronym gabril Jonathan Bowers ... group , all shown here in A sub 6 sub Coxeter plane orthographic projection s. Heptapeton family Notes ... more details
Birectified heptapeton Acronym bril Jonathan Bowers Coordinates The vertices of the birectified ... orthographic projection s. Heptapeton family Notes reflist References Harold Scott MacDonald Coxeter ... more details
Simplex is Latin for simple, pure, plain and may refer to Simplex , a term in geometry meaning an n dimensional analogue of a triangle 10 simplex , a hendecaxennon self dual regular 10 polytope Omnitruncated 6 simplex or omnitruncated heptapeton uniform 6 polytope Simplex graph American Simplex , an American automobile made in Mishawaka, Indiana, USA Bergmann Simplex , a compact firearm produced in the early 1900s Crane Simplex , a defunct luxury car manufacturer in New York, USA at the start of the 20th century Mercedes Simplex , an automobile model produced between 1902 and 1909 Pascal s simplex , a version of Pascal s triangle of more than three dimensions Sheffield Simplex , a British vehicle manufacturer operating 1907&ndash 1920 Simplex algorithm , a popular algorithm for numerical solution of linear programming problems Simplex circuit provides transmission in one direction only Simplex communication , a one way communications channel Simplex noise , a method for constructing an n dimensional noise function Simplex plot , a ternary plot used in game theory Simplex signaling , signaling in which two conductors are used for a single channel Herpes simplex is a viral disease caused by Herpes simplex virus es Simplex Amsterdam , a car manufacturer from the Netherlands Simplex bicycle , a French bicycle derailleur brand Simplex France , a French car manufacturer Simplex Birmingham , a British car manufacturer Simplex New Orleans , an American car manufacturer Simplex automobile , a car manufacturer from New York Simplex Turin , a car manufacturer from Italy Rex Simplex , a German car manufacturer Biology Simplex is commonly used in binominal names. Expand section date September 2011 SpeciesAbbreviation simplex Acartia simplex Amitostigma simplex Anisakis simplex Blanfordia simplex Firmiana simplex Herpes simplex virus Obesotoma simplex Paradiaptomus simplex Protanthea simplex See also Simplex was a trade name used by British railway locomotive manufacturers, ... more details
align right class wikitable width 320 Graphs of three List of regular polytopes Five dimensional regular polytopes and higher regular and three Uniform polypeton uniform polytopes align center valign top Image 6 simplex t0.svg 160px BR 6 simplex Heptapeton File 6 cube t5.svg 160px BR 6 orthoplex , 3 sub 11 sub align center valign top Image 6 cube t0.svg 160px BR 6 cube Hexeract Image 6 demicube t0 D6.svg 160px BR 6 demicube 1 sub 31 sub BR Demihexeract align center valign top Image E6 graph.svg 150px BR Gosset 2 21 polytope 2 sub 21 sub Image Gosset 1 22 polytope.svg 150px BR Gosset 1 22 polytope 1 sub 22 sub In Six dimensional space six dimensional geometry , a 6 polytope is a polytope , bounded by 5 polytope Facet mathematics facets . In the context of uniform polytope s, a 5 polytope A note on generality of terms for n polytopes and elements proposed name polypeton plural polypeta has been advocated, from the Greek language Greek root poly meaning many , a shortened Numerical prefix penta meaning five , and suffix on . Five refers to the dimension of the 5 polytope Facet mathematics facets . Definition A 6 polytope, or polypeton, is a closed six dimensional figure with Vertex geometry vertices , Edge geometry edges , face geometry faces , cell mathematics cells 3 faces , 4 faces, and 5 faces. A vertex is a Point geometry point where six or more edges meet. An edge is a line segment where four or more faces meet, and a face is a polygon where three or more cells meet. A cell is a polyhedron . A 4 face is a polychoron , and a 5 face is a polyteron . Furthermore, the following requirements must be met Each 4 face must join exactly two 5 faces facets . Adjacent facets are not in the same five dimensional hyperplane . The figure is not a compound of other figures which meet the requirements. Regular 6 polytopes Regular 6 polytopes can be generated from Coxeter group s represented by the Schl fli symbol p,q,r,s,t with t p,q,r,s polyteron Facet mathematics facets around ... more details
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