| Bitruncated 24-cell | ||
|---|---|---|
Schlegel diagram, centered on truncated cube, with alternate cells hidden |
||
| Type | Uniform polychoron | |
| Schläfli symbol | t1,2{3,4,3} | |
| Coxeter-Dynkin diagram | ||
| Cells | 48 (3.8.8) | |
| Faces | 336 | 192 {3} 144 {8} |
| Edges | 576 | |
| Vertices | 288 | |
| Edge figure | 3.8.8 | |
| Vertex figure | tetragonal disphenoid |
|
| Symmetry group | 2×F4 ], order 2304 | |
| Properties | convex, isogonal, isotoxal, isochoric | |
| Uniform index | 26 27 28 | |
The bitruncated 24-cell is a 4-dimensional uniform polytope (or uniform polychoron) derived from the 24-cell. It is constructed by bitruncating the 24-cell (truncating at halfway to the depth which would yield the dual 24-cell).
Being a uniform polychoron, it is vertex-transitive. In addition, it is cell-transitive, consisting of 48 truncated cubes, and also edge-transitive, with 3 truncated cubes cells per edge and with one triangle and two octagons around each edge.
The 48 cells of the bitruncated 24-cell correspond with the 24 cells and 24 vertices of the 24-cell. As such, the centers of the 48 cells form the root system of type F4.
Its vertex figure is a tetragonal disphenoid, a tetrahedron with 2 opposite edges length 1 and all 4 lateral edges length √(2+√2).
Read more about this topic: Truncated 24-cell