Dual pairs of polyhedra. Part 2

octahedron vs cube

What is the relationship between an octahedron and a cube?

These two polyhedra have the following fundamental parameters:

 

  Octahedron

  Hexahedron (cube)

The form of each side

  Triangle

  Square

Number of sides

  8

  6

Number of vertices

  6

  8

If we pay attention to the number of sides and vertices of these two polyhedra, then they are the opposite.

On the basis of a hexahedron, an octahedron can be constructed. To do this, we select the center of the face on each of the 6 faces of the hexahedron. By connecting all the centers together we obtain an octahedron. This obtained octahedron is exactly inscribed in the original hexahedron.

 

cube transform

A similar procedure can be done on an octahedron and get a cube out of it.
This property indicates that the octahedron and the hexahedron form a dual pair.

Video from our partners - the team "ART KOSEKOMA", clearly demonstrates this transformation.

An interesting feature in the transition from a cube to an octahedron is the appearance of three polyhedra belonging to the class of semi-regular ones, in other words Archimedean solids.

cube transform