0.00 $
 0 item(s)

Dual pairs of polyhedra. Part 2

What is the relationship between an octahedron and a cube?

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.

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.


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 bodies.


Polyhedron. What is it?

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

Dual pairs of polyhedra. Part 2

What is the relationship between an octahedron and a cube?

Polyhedra in architecture. Part 3. The Lighthouse of Alexandria

The Lighthouse of Alexandria, one of the Seven Wonders, was built in the 3d century BC in an...

Divide the icosahedron (into parts)

Is it possible to make up an icosahedron using more simple polyhedra?

Polyhedra in architecture. Part 4. Tower Syuyumbike

The most famous building in Kazan (city in Russia) and its main symbol is Tower Syuyumbike. It is...

Nets solids of revolution

What happens if a flat geometric shape, such as a rectangle, begins to rotate rapidly relative to...

Challenging task about a polyhedron

(challenging task called “a star”)