I wouldn't really call the 24-cell "a strange version" of the octahedron. It really isn't anything like any of the 3d Platonic solids. (It does have octahedral faces, though.)
http://fleetinbeing.net/hypersolid/examples/24cell.html
It doesn't bring out the cells or faces, but it does show edges in parallel coordinates. Edges show up as multi-points in the plot below. Above is a 3-d projection of the 24-cell which you can click+drag to rotate.