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:

 

  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, 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

Popular

Polyhedra in architecture. Part 4. Tower Syuyumbike

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

Prisms that saved the world

  The plot of the fantastic blockbuster "The Fifth Element", is built on the legend that there are...

Why can the paper be so strong?

Sometimes you hear the question: “Why did you choose paper (or more precisely, design cardboard) to...

Polyhedra in architecture. Alexandria Lighthouse

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

Birdhouse

Studio Artemy Lebedev (makes the design for the leading search engine Yandex) was the proposed...

Need More Jack-o'-lanterns? Maybe Archimedes Will Help Us?

The Great Archimedes is ready to help us. And it's great! According to legends, Archimedes created...

What Magic Edges issue to start from?

Suppose you first saw the edition “Magic Edges” on the counter of a bookstore or Internet...