24-cell

24-cell
Schlegel diagram (vertices and edges)
Type	Convex regular 4-polytope
Schläfli symbol	{3,4,3} r{3,3,4} = ${\displaystyle \left\{{\begin{array}{l}3\\3,4\end{array}}\right\}}$ {31,1,1} = ${\displaystyle \left\{{\begin{array}{l}3\\3\\3\end{array}}\right\}}$
Coxeter diagram	or or
Cells	24 {3,4}
Faces	96 {3}
Edges	96
Vertices	24
Vertex figure	Cube
Petrie polygon	dodecagon
Coxeter group	F4, [3,4,3], order 1152 B4, [4,3,3], order 384 D4, [31,1,1], order 192
Dual	Self-dual
Properties	convex, isogonal, isotoxal, isohedral
Uniform index	22

In four-dimensional geometry, the 24-cell is a convex regular 4-polytope, a four-dimensional analogue of a Platonic solid. It is named for the 24 octahedra that form its boundary.

It is also called C₂₄, or the icositetrachoron, octaplex (short for "octahedral complex"), icosatetrahedroid, octacube, hyper-diamond or polyoctahedron, being constructed of octahedral cells.