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2 21 polytope
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In 6-dimensional geometry, the 221 polytope is a uniform 6-polytope, constructed within the symmetry of the E6 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it an 6-ic semi-regular figure.[1] It is also called the Schläfli polytope.
![]() 221 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Rectified 221 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
![]() (122) ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
![]() Birectified 221 (Rectified 122) ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
orthogonal projections in E6 Coxeter plane |
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Its Coxeter symbol is 221, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of one of the 2-node sequences. He also studied[2] its connection with the 27 lines on the cubic surface, which are naturally in correspondence with the vertices of 221.
The rectified 221 is constructed by points at the mid-edges of the 221. The birectified 221 is constructed by points at the triangle face centers of the 221, and is the same as the rectified 122.
These polytopes are a part of family of 39 convex uniform polytopes in 6-dimensions, made of uniform 5-polytope facets and vertex figures, defined by all permutations of rings in this Coxeter-Dynkin diagram: .