Rectified 24-cell

In geometry, the rectified 24-cell or rectified icositetrachoron is a uniform 4-dimensional polytope (or uniform 4-polytope), which is bounded by 48 cells: 24 cubes, and 24 cuboctahedra. It can be obtained by rectification of the 24-cell, reducing its octahedral cells to cubes and cuboctahedra.

Rectified 24-cell
Schlegel diagram 8 of 24 cuboctahedral cells shown
Type	Uniform 4-polytope
Schläfli symbols	r{3,4,3} = ${\displaystyle \left\{{\begin{array}{l}3\\4,3\end{array}}\right\}}$ rr{3,3,4}=${\displaystyle r\left\{{\begin{array}{l}3\\3,4\end{array}}\right\}}$ r{31,1,1} = ${\displaystyle r\left\{{\begin{array}{l}3\\3\\3\end{array}}\right\}}$
Coxeter diagrams	or
Cells	48	24 3.4.3.4 24 4.4.4
Faces	240	96 {3} 144 {4}
Edges	288
Vertices	96
Vertex figure	Triangular prism
Symmetry groups	F4 [3,4,3], order 1152 B4 [3,3,4], order 384 D4 [31,1,1], order 192
Properties	convex, edge-transitive
Uniform index	22 23 24

E. L. Elte identified it in 1912 as a semiregular polytope, labeling it as tC₂₄.

It can also be considered a cantellated 16-cell with the lower symmetries B₄ = [3,3,4]. B₄ would lead to a bicoloring of the cuboctahedral cells into 8 and 16 each. It is also called a runcicantellated demitesseract in a D₄ symmetry, giving 3 colors of cells, 8 for each.