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Archimedes, a scientist from the Ancient Greece, discovered 13 types of polyhedra, called now as Archimedean solids, which are also referred 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 meets at each vertex. In the same order each of these solids can be inscribed into a sphere.
All these 13 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.
First of all, this is how all Archimedean solids look like:
1. Truncated tetrahedron  
2. Truncated octahedron  
3. Truncated hexahedron (or truncated cube)


4. Truncated dodecahedron  
5. Truncated icosahedron  
6. Cuboctahedron  
7. Rhombicuboctahedron  
8. Truncated cuboctahedron  
9. Snub cube  
10. Icosidodecahedron  
11. Truncated icosidodecahedron  
12. Truncated rhombicosidodecahedron  
13. Snub dodecahedron 
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 
One of the five Platonic polyhedra forms the basis for these 13 types of polyhedra.
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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 how the collection of polyhedra with the same side length will look like: