 321    
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 231
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 132 
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 Rectified 321
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 birectified 321
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 Rectified 231
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 Rectified 132 
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| Orthogonal projections in E7 Coxeter plane | |||||
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In 7-dimensional geometry, the 321 polytope is a uniform 7-polytope, constructed within the symmetry of the E7 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it an 7-ic semi-regular figure.[1]
Its Coxeter symbol is 321, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of the 3-node sequences.
The rectified 321 is constructed by points at the mid-edges of the 321. The birectified 321 is constructed by points at the triangle face centers of the 321. The trirectified 321 is constructed by points at the tetrahedral centers of the 321, and is the same as the rectified 132.
These polytopes are part of a family of 127 (27-1) convex uniform polytopes in 7-dimensions, made of uniform 6-polytope facets and vertex figures, defined by all permutations of rings in this Coxeter-Dynkin diagram: .
- ^ Gosset, 1900