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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.
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E 9 honeycomb. In geometry, an E9 honeycomb is a tessellation of uniform polytopes in hyperbolic 9-dimensional space. , also (E 10) is a paracompact hyperbolic group, so either facets or vertex figures will not be bounded. E 10 is last of the series of Coxeter groups with a bifurcated Coxeter-Dynkin diagram of lengths 6,2,1.
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 C 9 or [4,3 7] Coxeter group, and a lower symmetry with two copies of 8-orthoplex facets, alternating, with the D 9 or [3 6,1,1] Coxeter group.
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This oriented projection shows columns of vertices positioned a vertex-edge-vertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal's triangle, being 1:9:36:84:126:126:84:36:9:1 in the case of a 9-cube.
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