The vertices of the 24-cell, that is one of the six regular polytopes in dimension 4, are the centres of the faces of dimension 2 of a hypercube, here represented with a Schlegel diagram. In the figure, we see some of the 24 octahedra that form a 24-cell.
immagine di Gian Marco Todesco
The image belongs to the sections...:
24-cell (4D geometry)