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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.
A rectified cubic honeycomb – edges reduced to vertices, and vertices expanded into new cells. In Euclidean geometry, rectification, also known as critical truncation or complete-truncation, is the process of truncating a polytope by marking the midpoints of all its edges, and cutting off its vertices at those points. [1]
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.
In nine-dimensional geometry, a rectified 9-simplex is a convex uniform 9-polytope, being a rectification of the regular 9-simplex . These polytopes are part of a family of 271 uniform 9-polytopes with A 9 symmetry. There are unique 4 degrees of rectifications. Vertices of the rectified 9-simplex are located at the edge-centers of the 9-simplex.
The cuboctahedron is a rectified cube and also a rectified octahedron. It is also a cantellated tetrahedron. With this construction it is given the Wythoff symbol: 3 3 | 2. A skew cantellation of the tetrahedron produces a solid with faces parallel to those of the cuboctahedron, namely eight triangles of two sizes, and six rectangles.
Rectified 10-cubes. In ten-dimensional geometry, a rectified 10-cube is a convex uniform 10-polytope, being a rectification of the regular 10-cube . There are 10 rectifications of the 10-cube, with the zeroth being the 10-cube itself. Vertices of the rectified 10-cube are located at the edge-centers of the 10-cube.
Rectified 7-cubes. In seven-dimensional geometry, a rectified 7-cube is a convex uniform 7-polytope, being a rectification of the regular 7-cube . There are unique 7 degrees of rectifications, the zeroth being the 7-cube, and the 6th and last being the 7-cube. Vertices of the rectified 7-cube are located at the edge-centers of the 7-ocube.
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