I found a question based on an archemidean solid (truncated octahedron) in past IIT JEE question paper. Please elucidate archemidean solids- their types, total vertex, faces etc.

Dear Student,

Archimidean solids are semi regular convex polyhedrons which are composed of regular polygons meeting in identical vertices.

Check the following table:

Types	Faces	Faces	Vertices	Edges
Truncated tetrahedron	8	4 triangles 4 hexagons	12	18
Cuboctahedron	14	8 triangles 6 square	12	24
Truncated cube	14	8 triangles 6 octagons	24	36
Truncated octahedron	14	6 squares 8 hexagons	24	36
Rhombicuboctahedron	26	8 triangles 18 squares	24	48
Truncated cuboctahedron	26	12 squares 8 hexagons 6 octagons	48	72
Snub cube	38	32 triangles 6 squares	24	60
Icosidodecahedron	32	20 triangles 12 pentagons	30	60
Truncated dodecahedron	32	20 triangles 12 decagons	60	90
Truncated icosahedron	32	12 pentagons 20 hexagons	60	90
Rhombicosidodecahedron	62	20 triangles 30 squares 12 pentagons	60	120
Truncated icosidodecahedron	62	30 squares  20 hexagons 12 decagons	120	180
Snub dodecahedron	92	80 triangles 12 pentagons	60	150

Don't worry too much about these kind of questions. Keep your concepts clear and solve as many questions as possible. 

Hope it helps.

Regards