0.00 $
 0 item(s)

Dual pairs of polyhedra

dodecahedron vs icosahedron

What does 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, 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.


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


Richard Sweeney's worlds

Young British designer, Richard Sweeney, creates amazing paper sculptures. It is interesting that...

Polyhedra made of ribbon

The article in “Science and Life” (1989, №6, Cherenkov A. Khramov V.) tells about an interesting way...

Polyhedron. What is it?

A polyhedron is a solid bounded by flat polygons, which are called faces. The sides of the faces are...

Novotalitskaya school

Under the guidance of Tatyana Yurievna Timofeyeva, a teacher of mathematics, the guys worked on...

The soccer ball is the main participant of the 2018 World Cup

It is round, but nobody canceled the shape...

The most durable construction

Which geometric solid known to us has the greatest strength? Which is most resistant to external...

Paper nets are must in Mcdonalds

Boxes for Big Mac and potatoes familiar to everyone from childhood, a glass for Coca-Cola is also...