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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. Vertices of the ...
In nine-dimensional geometry, a rectified 9-simplex is a convex uniform 9-polytope, being a rectification of the regular 9-orthoplex. There are 9 rectifications of the 9-orthoplex. Vertices of the rectified 9-orthoplex are located at the edge-centers of the 9-orthoplex.
This 9-cube graph is an orthogonal projection. This orientation 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.
Regular n-polytopes have n orders of rectification.The zeroth rectification is the original form. The (n−1)-th rectification is the dual.A rectification reduces edges to vertices, a birectification reduces faces to vertices, a trirectification reduces cells to vertices, a quadirectification reduces 4-faces to vertices, a quintirectification reduced 5-faces to vertices, and so on.
The icosahedron, snub cube and snub dodecahedron are the only three convex ones. They are obtained by snubification of the truncated octahedron, truncated cuboctahedron and the truncated icosidodecahedron - the three convex truncated quasiregular polyhedra. The only snub polyhedron with the chiral octahedral group of symmetries is the snub cube.
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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.