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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.
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 facets .
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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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.
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