Archimedes, a scientist from Ancient Greece, discovered thirteen types of polyhedra, now called Archimedean solids, which are also referred to as semiregular polyhedra.
Each of them is limited by different types of regular polygons where the polyhedral angles and identical polygons are equal. Furthermore, the same number of equal faces meet at each vertex. In the same order, each of these solids can be inscribed into a sphere.
All these thirteen names make your head spin when you see them for the first time. However, it is possible to sort things out, understand and remember them.
What all Archimedean solids look like
3. Truncated hexahedron (or truncated cube)
4. Truncated dodecahedron
8. Truncated cuboctahedron
11. Truncated icosidodecahedron (Small rhombicosidodecahedron)
12. Truncated rhombicosidodecahedron
How is the name of the polyhedron formed?
Pay attention to the fact that there is a wordbasis for every type of polyhedron which forms their names. It is this wordbasis that helps to classify the current polyhedra to one of the five regular polyhedra.
Name 
Wordbasis

Truncated tetrahedron

tetrahedron 
Truncated octahedron
Cuboctahedron
Rhombicuboctahedron
Truncated cuboctahedron

octahedron 
Truncated cube
Snub cube

cube 
Truncated dodecahedron
Icosidodecahedron
Truncated icosidodecahedron
Truncated rhombicosidodecahedron
Snub dodecahedron

dodecahedron 
Truncated icosahedron

icosahedron 
Which polyhedra forms the basis?
One of the five Platonic polyhedra forms the basis for these 13 types of polyhedra.
What geometric figures can be used to construct Archimedean polyhedra?
All types of Archemedean polyhedra can consist of a certain set of regular.
1. Truncated tetrahedron : 4 triangles + 4 hexagons
= 4
+ 4
2. Truncated octahedron: 6 squares + 8 hexagons
= 6
+ 8
3. Truncated hexahedron (or truncated cube): 8 triangles + 6 octagons
= 8
+ 6
4. Truncated dodecahedron: 20 triangles + 12 decagon
= 20
+ 12
5. Truncated icosahedron: 12 pentagons + 20 hexagons
= 12
+ 20
6. Cuboctahedron: 8 triangles + 6 squares
= 8
+ 6
7. Rhombicuboctahedron: 8 triangles + 18 squares
= 8
+ 18
8. Truncated cuboctahedron: 12 squares + 8 hexagons + 6 octagons
= 12
+ 8
+ 6
9. Snub cube: 32 triangles + 6 squares
= 32
+ 6
10. Icosidodecahedron: 20 triangles + 12 pentagons
= 20
+ 12
11. Truncated icosidodecahedron: 20 triangles + 30 squares + 12 pentagons
= 20
+ 30
+ 12
12. Truncated rhombicosidodecahedron: 30 squares + 20 hexagons + 12 decagons
= 30
+ 20
+ 12
13. Snub dodecahedron: 80 triangles + 12 pentagons
= 80
+ 12
The size of a polyhedra
To create a collection of polyhedra, we need to adhere to certain conditions, so that sizes will be comparable and models can easily be compared with each other.
One of the options is to create a model which fits into the sphere of the standard sizes. Then all 13 polyhedra will look like this:
Another option is to set up the same length for the side of all the polygons which will be used in the model. The proportion of polygons with the same side length is:
 Triangle;
 Square;
 Pentagon;
 Hexagon;
 Octagon;
 Decagon.
This is what the collection of polyhedra with the same side length will look like:
Where to find the nets of Archimedean solids
Nets for all thirteen Archimedes polyhedra can be found in the kit "Magic Edges":
Magic Edges № 18
 Truncated tetrahedron;
 Truncated octahedron;
 Truncated cube;
 Cuboctahedron.
Magic Edges № 19
 Truncated icosahedron;
 Icosidodecahedron;
_
_
Magic Edges № 21
 Rhombicuboctahedron;
 Truncated cuboctahedron
Magic Edges № 27
 Truncated dodecahedron;
 Truncated icosidodecahedron
Magic Edges № 29
 Snub cube;
 Snub dodecahedron
Preparing for release:
Magic Edges № 31 (Truncated rhombicosidodecahedron)