In 4D there are 6, the five expected ones and an additional strange version of the octahedron.
In 5D and more, there are only 3, the equivalents of the tetrahedron, cube and octahedron.
In 5D and more, there are only 3, the equivalents of the tetrahedron, cube and octahedron.
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.