Unlike Platonic solids, Archimedean solids can have multiple regular polygons as their faces.
Truncated Tetrahedron
(3.6.6)
Vertices = 12
Edges = 18
Faces = 8
(4 triangles, 4 hexagons)
Cuboctahedron
(3.4.3.4)
Vertices = 12
Edges = 24
Faces = 14
(8 triangles, 6 squares)
Truncated Cube
(3.8.8)
Vertices = 24
Edges = 36
Faces = 14
(8 triangles, 6 octagons)
Truncated Octahedron
(4.6.6)
Vertices = 24
Edges = 36
Faces = 14
(6 squares, 8 hexagons)
Rhombi-cuboctahedron
(3.4.4.4)
Vertices = 24
Edges = 48
Faces = 26
(8 triangles, 18 squares)
Truncated Cuboctahedron
(4.6.8)
Vertices = 48
Edges = 72
Faces = 26
(12 squares, 8 hexagons, 6 octagons)
Snub Cube
(3.3.3.3.4)
Vertices = 24
Edges = 60
Faces = 38
(32 triangles, 6 squares)
Icosi-dodecahedron
(3.5.3.5)
Vertices = 30
Edges = 60
Faces = 32
(20 triangles, 12 pentagons)
Truncated Dodecahedron
(3.10.10)
Vertices = 60
Edges = 90
Faces = 32
(20 triangles, 12 hexagons)
Truncated Icosahedron
(5.6.6)
Vertices = 60
Edges = 90
Faces = 32
(12 petagons, 20 hexagons)
Rhombicosi-dodecahedron
(3.4.5.4)
Vertices = 60
Edges = 120
Faces = 62
(20 triangles, 30 squares, 12 pentagons)
Truncated Icosi-dodecahedron
(4.6.10)
Vertices = 120
Edges = 180
Faces = 62
(30 squares, 20 hexagons, 12 decagons)
Snub Dodecahedron
(3.3.3.3.5)
Vertices = 60
Edges = 150
Faces = 92
(80 triangles, 12 pentagons)
All images found here: https://en.wikipedia.org/wiki/Archimedean_solid