Recently, I was thinking about the 4-d partial Stott expansion series from hex to sidpith. In particular, the lace tower descriptions of those. I figured out that:

hex = pt || oct || pt

pex hex = pt || oct || oct || pt, or line || esquidpy || line

quawros = line || esquidpy || esquidpy || line, or square || squobcu || square

pacsid pith = square || squobcu || squobcu || square, or cube || sirco || cube

sidpith = cube || sirco || sirco || cube

In particular, this should mean that there should be a series from the oct pyramid to cube || sirco.

Specifically:

Start with octpy (oct pyramid). this has as cells 1 oct (octahedron) + 8 tets (tetrahedra).

The next one is line || esquidpy. This can also be thought of as a square pyramidal prism with two square pyramidal pyramids on the bases. Its cells are 1 esquidpy (elongated square dipyramid) + 8 tets + 4 trips (triangular prisms).

The next one is square || squobcu. It is formed by joining 2 square || squacu together at a cupola. Its cells are 1 squobcu (square orthobicupola) + 2 cubes + 8 tets + 8 trips.

And finally there is cube || sirco, with cells 1 cube (top) + 6 cubes (sides) + 8 tets + 12 trips + 1 sirco (small rhombicuboctahedron).

Is this a valid partial expansion series, and are there any others like it?