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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 {4,3 7 }, being composed of three 8-cubes around each 7-face.
Truncated 9-demicube. 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 facets .
Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions n as an n -dimensional polytope or n-polytope. For example, a two-dimensional polygon is a 2-polytope and a three-dimensional polyhedron is a 3-polytope.
Rectified 9-cubes. 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.
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 HM 9 for a 9-dimensional half measure polytope.
The following list of polygons, polyhedra and polytopes gives the names of various classes of polytopes and lists some specific examples. Polytope elements [ edit ] Polygon (2-polytope) [ edit ]
The cross-polytope is the convex hull of its vertices. The n -dimensional cross-polytope can also be defined as the closed unit ball (or, according to some authors, its boundary) in the ℓ 1 -norm on Rn : In 1 dimension the cross-polytope is simply the line segment [−1, +1], in 2 dimensions it is a square (or diamond) with vertices { (±1, 0 ...
Definition. A 4-polytope is a closed four-dimensional figure. It comprises vertices (corner points), edges, faces and cells. A cell is the three-dimensional analogue of a face, and is therefore a polyhedron. Each face must join exactly two cells, analogous to the way in which each edge of a polyhedron joins just two faces.