Interesting web site, but I didn't see any reference to the stated claim. Perhaps you can point me in the right direction?
Also, I'm curious exactly how "semi-regular" is defined? Does it mean that all faces are isomorphic but that edges and vertices are not? The Archimedian solids do not meet this qualification as they have different kinds of faces, but solids with such quality may be constructed with any desired even number of faces (examine a D10 and extend the principle as desired). To be sure, producing a D24 by this method would be sorta iffy; producing a D114 by this method would be crazy. Can't see anything to prevent it, though.
While this article sounds like a spoof, I'm curious whether anyone has actually marketed a good D24? I've seen a D30 and a D60 [for the latter, take a dodecahedron and replace each face with five triangular ones; for the former, do the above but then nuke the central edge from each face and reshape things to flatten them] but am not clear how one could make a roundish D24.