0.00 $
 0 item(s)

Dual pairs of polyhedra

dodecahedron vs icosahedron

What do the dodecahedron and icosahedron have in common?

These two polyhedra have the following fundamental parameters:




The form of each side



Number of sides



Number of vertices



If we pay attention to the number of sides and vertices of these two polyhedra, they are the opposite.
What does this mean for us? Based on a dodecahedron, an icosahedron can be constructed.
To do this, on each of the 12 faces of the dodecahedron, we select the face center. By connecting all the centers, we obtain an icosahedron. This obtained icosahedron will be exactly inscribed in the original dodecahedron.

dodecahedron transform

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 semi-regular words, in other words, Archimedean solids.

dodecahedron transform


An article in the journal Science and Life

One of the most famous magazines in Russia - popularizers of science with 115 years of history-...

Polyhedra in architecture. Part 1

Architectural masterpieces located in different parts of the world reflect the human soul. Secret...

The magic of "Yin" and "Yang" in the polyhedra

There is a concept that a polyhedron's vertex gives off energy, and the plane absorbs energy. In...

Richard Sweeney's worlds

Young British designer, Richard Sweeney, creates amazing paper sculptures. Interestingly, regular...

Polyhedra in a computer game

It is not often possible to encounter polyhedra outside of math textbooks. Even though such...

Moscow School 2005

Is it possible to conduct additional school classes in geometry collecting models of polyhedra? Of...

Multifaceted hearth

For a primeval man, fire once became a new form of social life. The night ceased to be an...