These include: A further source of confusion lies in the way that the Archimedean solids are defined, again with different interpretations appearing.
Gosset's definition of semiregular includes figures of higher symmetry: the regular and quasiregular polyhedra.
Johannes Kepler coined the category semiregular in his book Harmonices Mundi (1619), including the 13 Archimedean solids, two infinite families (prisms and antiprisms on regular bases), and two edge-transitive Catalan solids, the rhombic dodecahedron and rhombic triacontahedron.
The trigonal trapezohedron, a topological cube with congruent rhombic faces, would also qualify as semiregular, though Kepler did not mention it specifically.
We can distinguish between the facially-regular and vertex-transitive figures based on Gosset, and their vertically-regular (or versi-regular) and facially-transitive duals.
By implication this treats the Catalans as not semiregular, thus effectively contradicting (or at least confusing) the definition he provided in the earlier footnote.