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The rotation of the polyhedron "The ninth stellated form icosahedron" from the details of the set "Magic Edges 28"

The release of the set to the end of November 2018.

fest nauk18October 12-14, 2018. A science festival will be held in Moscow - "Science 0+"

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DSCF0188Moscow Press Festival 2018

On September 1, in the Victory Park on Poklonnaya Hill, we will take part in the 16th Moscow Press Festival.

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matematukum2018 1On September 30, 2018, the best educational projects of Moscow will gather at one site, and through workshops, lectures and interactive tasks, they will help you to understand and love mathematics.

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Archimedean polyhedra

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Archimedes, a scientist from the Ancient Greece, discovered 13 types of polyhedra, called now as Archimedean solids, which are also referred as semi-regular polyhedra.

Each of them is limited by different types of regular polygons where the polyhedral angles and identical polygons are equal. Furthermore, the same number of equal faces meets at each vertex. In the same order each of these solids can be inscribed into a sphere.

Natural polyhedra

Natural polyhedra

In natural environments regular polyhedra can be found in the form of crystals (minerals). 
Sodium sulphate reminds the shape of tetrahedron.

Practical use of paper models

Quite often a question about a practical use of paper models pops up.  What is the point of paper modeling?

Mathematical properties of the Platonic solids

One can specify the following mathematical characteristics in each of the five Platonic solids:

1. The radius of the sphere circumscribing the polyhedron;

2. The radius of the sphere inscribed in the polyhedron;

3. The surface area of the polyhedron;

4. The volume of the polyhedron.

Polyhedron. What is it?

A polyhedron is a solid bounded by flat polygons, which are called faces. Sides of the faces are called edges, and their corners are called as vertices. Depending on the number of faces one can specify tetrahedron (4 faces), pentahedron (5 faces), etc. A polyhedron is considered to be convex if it is located on one side of the plane of each of its faces. A polyhedron is called regular if its faces are regular polygons (i.e., where all sides and angles are equal) and all polyhedral angles at the vertices are equal. There can be found five types of regular polyhedra: tetrahedron, cube (regular hexahedron), octahedron, dodecahedron, icosahedron. 

Polyhedra in architecture. Part 5


Architects have used the elements of polyhedra in designing their constructions since ancient times. Nowadays this approach distinguishes buildings among thousands of others.

The Ministry of Defense in USA has the shape of a regular pentagon.

Divide the icosahedron (into parts)

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

Stellated octahedron - a challenging task

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A new and unusual way of making a model of Stellated polyhedron was discovered by a German mathematician and astronomer Johannes Kepler in 1619. 


icosahedron Birdhouse

Art. Lebedev Studio has offered a new birdhouse in the form of polyhedron.


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

Mathematicians have already proved the possibility of making 3D objects from a ribbon. You can see how to make a tetrahedron in Figure 1. The ribbon is folded according to the drawn lines, sides of equilateral triangles.

One can make a cube using a similar way (see Fig. 2). Its faces are lined up in a chain, and in order to change the direction of the ribbon to complete the formation, it is enough just to fold it on the diagonal of the square (the article about a cube made of ribbon was published in “Science and Life”, №10, 1972)