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:



  Hexahedron (cube)

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.

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


How to assemble polyhedra without glue?

So far, we have actively used glue to assemble polyhedrons from the Magic Edges sets. Moreover, we...

A Note on Archimedes - Ancient Greek Scientist

ARCHIMED (287 - 212 BC) - Ancient Greek mathematician, physicist and mechanic. Archimedes is the...

Master of Technology

In this article we will introduce you to the technology of manufacturing geometric metal solids,...

How to master stereometry?

In geometry the section which deals with three-dimensional figures is called stereometry. The word...

The star of hope

A star is an image of divine idea and will, due to them our Light and Universe were created and...

Polyhedra in architecture. Part 2

The “business card” of the Republic of Belarus is a new building of the National Library in Minsk....

Polyhedra made of ribbon

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