A 24-cell
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. 6 of these points are the vertices of the dual octahedron of the "big" cube (in the diagram), 6 are the vertices of the dual octahedron of the "small" cube (in the diagram), the other 12 vertices are the vertices of a cuboctahedron (the one represented in the figure).
© matematita
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24-cell (4D geometry)
