The definition I am using from Wikipedia is:

an Archimedean solid is one of the 13 solids first enumerated by Archimedes. They are the semi-regular convex polyhedra composed of regular polygons meeting in identical vertices, excluding the 5 Platonic solids (which are composed of only one type of polygon) and excluding the prisms and antiprisms. They differ from the Johnson solids, whose regular polygonal faces do not meet in identical vertices

But looking at the picture of a truncated icosidodecahedron there are light and dark gray vertices that if I use a right hand rule are (4,6,10) for dark and (4,10,6) for light.

Same for the truncated cuboctahedron, which is listed as have (4,6,8) vertex figure, but seems to have that split between (4,6,8) and (4,8,6).

Does this silly nitpick I have mean anything?