0.00 $
 0 item(s)

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, they are the opposite.

Based on 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, 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


Polyhedron Chandelier

A suspended ceiling lamp, or simply a chandelier, has never been so close to exact mathematical...

Merkaba - energy polyhedron

According to some spiritual teachings, a polyhedron already familiar to us — a compound of two...

Polyhedra - Interior Items

Polyhedra can be an ornament to your home, creating a zest in the...

Rhombic dodecahedron 3D Calendar for 2021

The invention of the calendar is a remarkable event for humanity. The fact that a year consists of...

Calendar - dodecahedron

What do you think...

Archimedean Polyhedra. How to make pdf template

Archimedes, a scientist from Ancient Greece, discovered thirteen types of polyhedra, now called...

Regular Polyhedrons. How to make pdf template

There are five regular polyhedra: a tetrahedron, an octahedron, a cube (also known as a...