 9-orthoplex    
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 Rectified 9-orthoplex
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 Birectified 9-orthoplex
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 Trirectified 9-orthoplex
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 Quadrirectified 9-cube
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 Trirectified 9-cube
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 Birectified 9-cube
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 Rectified 9-cube
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 9-cube
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| Orthogonal projections in BC9 Coxeter plane | |||
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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 birectified 9-cube are located in the square face centers of the 9-cube. Vertices of the trirectified 9-orthoplex are located in the cube cell centers of the 9-cube. Vertices of the quadrirectified 9-cube are located in the tesseract centers of the 9-cube.
These polytopes are part of a family 511 uniform 9-polytopes with BC9 symmetry.