In the octahedron centered projection of the runcinated 24-cell, are the 12 equatorial octahedra projected onto rhombi? In this case I guess the projected 3d-envelope shoud correspond to the polyhedron where these planar octahedra become flattened rhombi with diagonals 1 and Sqrt(2) as shown in the attached image. Is this correct? I do not see the planes clearly in the cell decomposition
http://eusebeia.dyndns.org/4d/runci24cell, they could be two triangles slightly folded instead of a rhombus?