Spherixals, or Spherical Volumetric rendering is actually rather a nutty idea of mine. If you read my previous post. It means that instead of having 4 sides to represent a voxel object, and mip maps of them and the multiple layers of maps, you only need the sphere map and sphere layers.
I think they have a lot going for them. They do need a hi res mesh is needed close up, but I think that the same can be said for voxels. Spherixals can be rendered using bilinear height filtering. They can have details applied. They can be procedurally generated. They can have multiple passes. They can have fogged rather easily (and rather quickly). They could be used as fog volumes too, with a little thought.
Volumetrics like the one above are rather interesting. They could create rather odd shapes, and such. One possible use I can think of is shadowed volumetric light. Think of a green glow. It is through a gas or something. There is a rather large grill obscuring portions of this. So as you walk past a normal occurance of this. You would get some rather odd effects. Volumetrics like spherixals on the other hand could render them fine.
One rather odd idea I did have though, was using spherixals to represent normal lights. This one is a little bit odd, because effectively it is using saved pregenerated rays.
One sphere map would be needed per point light. Then, at each point on the map, you shoot a ray in that direction of the normal of the sphere (your sphere is constant). You record the distance to the the polygon it struck. This can be precalculated. At that point, the opposite of the original normal from the sphere, is then the light vector in unit form.
Of course, this could be used to do shadows as well... But there is a flaw in that, if you do, you could end up with a shadow holes. So I recommend using a pregenerated set of only the lighted polygons.