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What does the dodecahedron and icosahedron have in common?
These two polyhedra have the following fundamental parameters:
Dodecahedron 
Icosahedron 

The form of each side 
Pentagon 
Triangle 
Number of sides 
12 
20 
Number of vertices 
20 
12 
If we pay attention to the number of sides and vertices of these two polyhedra, then they are the opposite.
What does this mean for us? On the basis of a dodecahedron, an icosahedron can be constructed.
To do this, on each of the 12 faces of the dodecahedron, we select the center of the face. By connecting all the centers together we obtain an icosahedron. This obtained icosahedron will be exactly inscribed in the original dodecahedron.
A similar procedure can be performed on an icosahedron and obtained from it a dodecahedron.
This property indicates that the icosahedron and the dodecahedron form a dual pair.
Video from our partners  the team "ART KOSEKOMA", clearly demonstrates this transformation.
An interesting feature in the transition from a dodecahedron to an icosahedron is the emergence of three polyhedra belonging to the class of semiregular words in other words Archimedean bodies.
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