Yesterday, an idea occurred to me w.r.t. finding CRFs via cut-n-paste operations. So far, the only cut-n-paste operations that we've really explored in depth is only augmentation/diminishing of uniform polychora (and that's still far from complete), and stacks of segmentochora.

So I thought, what about a parallel to the gluing of the 600-cell lunes to make a 600-cell? But let's say we relax the requirement that the lunes be CRF, as long as the result of gluing them is CRF (and closes up properly). That got me thinking about 3D shapes that could potentially be formed this way, so I thought of cutting up the icosidodecahedron (o5x3o):

We already know that this can be cut into two pentagonal rotunda. Now, look at the vertex-first projection:

This shows that we can actually cut o5x3o into four pieces, which are lune-like shapes containing bisected decagons, that come in two opposite pairs. Let's call the two kinds of lunes piece A and piece B. So in clockwise order, the icosidodecahedron can be reconstituted by gluing together A-B-A-B. But the interfaces between them are bisected decagons, so that means if we rearrange the order of gluing to A-A-B-B, the shape should still close up! And since all of the bisected decagons will be internal, shouldn't that mean the result will be CRF?

So my question is, why isn't this shape in Johnson's list (or is it)? Is there some unexpected non-convexity going on here?