2 41 polytope

Its Coxeter symbol is 241, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end of the 2-node sequences.

The birectified 241 is constructed by points at the triangle face centers of the 241, and is the same as the rectified 142.

This polytope is a facet in the uniform tessellation, 251 with Coxeter-Dynkin diagram: The 2160 vertices can be defined as follows: It is created by a Wythoff construction upon a set of 8 hyperplane mirrors in 8-dimensional space.

Seen in a configuration matrix, the element counts can be derived by mirror removal and ratios of Coxeter group orders.

240 t1(221) 17280 t1{36} 2160 141 The rectified 241 is a rectification of the 241 polytope, with vertices positioned at the mid-edges of the 241.

It is created by a Wythoff construction upon a set of 8 hyperplane mirrors in 8-dimensional space, defined by root vectors of the E8 Coxeter group.

The projection of 2 41 to the E 8 Coxeter plane (aka. the Petrie projection) with polytope radius and 69120 edges of length
Shown in 3D projection using the basis vectors [u,v,w] giving H3 symmetry:
  • u = (1, φ , 0, −1, φ , 0,0,0)
  • v = ( φ , 0, 1, φ , 0, −1,0,0)
  • w = (0, 1, φ , 0, −1, φ ,0,0)
The 2160 projected 2 41 polytope vertices are sorted and tallied by their 3D norm generating the increasingly transparent hulls for each set of tallied norms. The overlapping vertices are color coded by overlap count. Also shown is a list of each hull group, the normed distance from the origin, and the number of vertices in the group.
The 2160 projected 2 41 polytope projected to 3D (as above) with each normed hull group listed individually with vertex counts. Notice the last two outer hulls are a combination of two overlapped Icosahedrons (24) and a Icosidodecahedron (30).