I noticed that http://hddb.teamikaria.com/wiki/CRFP4DP/Diminishings lists 7 rotundas. Two of these, stauroperihedral rotunda and rhodoperihedral rotunda are created by slicing of prismatotruncated tesseract/prismatotruncated 120-cell.

My research of tetrahedral vertices led me to vertex "346-646", consisting of triangular cupola, truncated tetrahedron, hexagonal prism and truncated octahedron. This is a part of "pyroperihedral rotunda", a diminishing of prismatotruncated pentachoron x3x3o3x.

Now, this wasn't considered a rotunda because it's bigger than the other part of the slice (truncated tetrahedron || truncated octahedron or tetrahedral canticupola); however, I'd argue otherwise. The key fact is that is we cut prismatotruncated pentachoron in truncated octahedral slice, we'll get two polychora that do not "bulge" -- i.e. their maximum 3D diameter is in the hyperplane of the cut. Or, in other words, two copies of a polychoron with this property can be glued together to form another convex polychoron. This means that prismatotruncated pentachoron can be considered a "cupolarotunda", a part of small family including tetrahedral canticupola, pyroperihedral rotunda and various bicupolas, birotundas, cupolarotundas and their elongated versions.

Therefore, I submit that this polychoron should be counted as a rotunda in its own right and not just as a diminishing.