Archimedean SemiRegular Polyhedra
The Archimedean polyhedra are listed
here according to which symmetry class
the polyhedron belongs to.

tetrahedral symmetry

cuboctahedral symmetry

(3,4,3,4) cuboctahedron

(4,6,6) truncated octahedron

(3,8,8) truncated cube

(3,4,4,4) rhombicuboctahedron,
often called the small rhombicuboctahedron

(4,6,8) truncated cuboctahedron,
often called the great rhombicuboctahedron

(3,3,3,3,4) snub cube, better
called the snub cuboctahedron

icosidodecahedral symmetry

(3,5,3,5) icosidodecahedron

(5,6,6) truncated icosahedron

(3,10,10) truncated dodecahedron

(3,4,5,4) rhombicosidodecahedron,
often called the small rhombicosidodecahedron

(4,6,10) truncated icosidodecahedron,
often called the great rhombicosidodecahedron

(3,3,3,3,5) snub dodecahedron,
better called the snub icosidodecahedron