Symmetry Constructions
There are three different symmetry constructions of this polytope. The lowest construction can be doubled into by adding a mirror that maps the bifurcating nodes onto each other. can be mapped up to symmetry by adding two mirror that map all three end nodes together.
The vertex figure is a triangular prism, containing two cubes and three cuboctahedra. The three symmetries can be seen with 3 colored cuboctahedra in the lowest construction, and two colors (1:2 ratio) in, and all identical cuboctahedra in .
| Coxeter group | = | = | = |
|---|---|---|---|
| Order | 1152 | 384 | 192 |
| Full symmetry group |
<> = ] = |
||
| Coxeter-Dynkin diagram | |||
| Facets | 3: 2: |
2,2: 2: |
1,1,1: 2: |
| Vertex figure |
Read more about this topic: Rectified 24-cell
Famous quotes containing the word symmetry:
“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.”
—George Gordon Noel Byron (1788–1824)