|
Runcicantitruncated 7-simplex
In seven-dimensional geometry, a runcinated 7-simplex is a convex uniform 7-polytope with 3rd order truncations (runcination) of the regular 7-simplex. There are 8 unique runcinations of the 7-simplex with permutations of truncations, and cantellations. Runcinated 7-simplex Alternate names * Small prismated octaexon (acronym: spo) (Jonathan Bowers) Coordinates The vertices of the ''runcinated 7-simplex'' can be most simply positioned in 8-space as permutations of (0,0,0,0,1,1,1,2). This construction is based on facets of the runcinated 8-orthoplex. Images Biruncinated 7-simplex Alternate names * Small biprismated octaexon (sibpo) (Jonathan Bowers) Coordinates The vertices of the ''biruncinated 7-simplex'' can be most simply positioned in 8-space as permutations of (0,0,0,1,1,1,2,2). This construction is based on facets of the biruncinated 8-orthoplex. Images Runcitruncated 7-simplex Alternate names * Prismatotruncated octaexon (acronym: patto) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
7-simplex T0
In seven-dimensional space, 7-dimensional geometry, a 7-simplex is a self-dual Regular polytope, regular 7-polytope. It has 8 vertex (geometry), vertices, 28 Edge (geometry), edges, 56 triangle Face (geometry), faces, 70 tetrahedral Cell (mathematics), cells, 56 5-cell 5-faces, 28 5-simplex 6-faces, and 8 6-simplex 7-faces. Its dihedral angle is cos−1(1/7), or approximately 81.79°. Alternate names It can also be called an octaexon, or octa-7-tope, as an 8-facet (geometry), facetted polytope in 7-dimensions. The 5-polytope#A note on generality of terms for n-polytopes and elements, name ''octaexon'' is derived from ''octa'' for eight Facet (mathematics), facets in Greek language, Greek and exa, ''-ex'' for having six-dimensional facets, and ''-on''. Jonathan Bowers gives an octaexon the acronym oca. As a configuration This Regular 4-polytope#As configurations, configuration matrix represents the 7-simplex. The rows and columns correspond to vertices, edges, faces, cells, 4-fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harold Scott MacDonald Coxeter
Harold Scott MacDonald "Donald" Coxeter (9 February 1907 – 31 March 2003) was a British-Canadian geometer and mathematician. He is regarded as one of the greatest geometers of the 20th century. Coxeter was born in England and educated at the University of Cambridge, with student visits to Princeton University. He worked for 60 years at the University of Toronto in Canada, from 1936 until his retirement in 1996, becoming a full professor there in 1948. His many honours included membership in the Royal Society of Canada, the Royal Society, and the Order of Canada. He was an author of 12 books, including '' The Fifty-Nine Icosahedra'' (1938) and '' Regular Polytopes'' (1947). Many concepts in geometry and group theory are named after him, including the Coxeter graph, Coxeter groups, Coxeter's loxodromic sequence of tangent circles, Coxeter–Dynkin diagrams, and the Todd–Coxeter algorithm. Biography Coxeter was born in Kensington, England, to Harold Samuel Coxete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Runcinated 8-orthoplex
In geometry, runcination is an operation that cuts a regular polytope (or honeycomb) simultaneously along the faces, edges, and vertices, creating new facets in place of the original face, edge, and vertex centers. It is a higher order truncation operation, following cantellation, and truncation. It is represented by an extended Schläfli symbol t0,3. This operation only exists for 4-polytopes or higher. This operation is dual-symmetric for regular uniform 4-polytopes and 3-space convex uniform honeycombs. For a regular 4-polytope, the original cells remain, but become separated. The gaps at the separated faces become p-gonal prisms. The gaps between the separated edges become r-gonal prisms. The gaps between the separated vertices become cells. The vertex figure for a regular 4-polytope is an ''q''-gonal antiprism (called an ''antipodium'' if ''p'' and ''r'' are different). For regular 4-polytopes/honeycombs, this operation is also called expansion by Alicia Boole Stott ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. More specifically: * In three-dimensional geometry, some authors call a facet of a polyhedron any polygon whose corners are vertices of the polyhedron, including polygons that are not ''Face (geometry), faces''. To ''facetting, 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 higher-dimensional polytopes. * In polyhedral combinatorics and in the general theory of polytopes, a Face (geometry), face that has dimension ''n'' − 1 (an (''n'' − 1)-face or hyperface) is called a Face (geometry)#Facet, facet. In this terminology, every facet is a face. * A facet of a simplicial complex is a maximal simplex, that is a simplex that is not a face of another simplex of the complex.. For (boundary complex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
