User:Jgmoxness/sandbox

In geometry, the dual Snub_24-cell is a convex uniform 4-polytope composed of 96 regular cells. Each cell has faces of two kinds: 3 kites and 6 isosceles triangles. The polytope has a total of 432 faces (144 kites and 288 isosceles triangles) and 480 edges.

Semiregular polytope
It was discovered by Koca et al. in a 2011 paper.

Coordinates
The vertices of a dual snub 24-cell are obtained through non-commutative multiplication of the simple roots (T') used in the quaternion base generation of the 600 vertices of the 120-cell. The following orbits of weights of D4 under the Weyl group W(D4): O(0100) : T = {±1,±e1,±e2,±e3,(±1±e1±e2±e3)/2} O(1000) : V1 O(0010) : V2 O(0001) : V3



Constructions
One can build it from the subsets of the 120-cell, namely the 24 vertices of T=24-cell, 24 vertices of the alternate T'=D4 24-cell, and 96 vertices of the alternate snub 24-cell S'=T'undefined using the quaternion construction of the 120-cell and non-commutative multiplication.

Dual
The dual polytope of this polytope is the Snub 24-cell.