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Truncated icosahedron

Truncated  icosahedron

A polyhedron is obtained by successively cutting off each of the vertices of the icosahedron.

A truncated icosahedron is a semiregular convex polyhedron with two properties:
1. All faces are regular polygons of two types - a hexagon and a pentagon;
2. For any pair of vertices, there is a symmetry of the polyhedron (that is, a motion that translates the polyhedron into itself) that transforms one vertex to another.

Archimedes

The truncated icosahedron is one of the 13 solids of Archimedes.

Archimedean solids are semiregular polyhedra in the sense that their faces are regular polygons. Still, they are not the same, while the condition of one of the types of spatial symmetry: tetrahedral, octahedral, or icosahedral is preserved.

The main feature of this polyhedron is that its shape served as the basis for football manufacture. This becomes apparent after applying the black and white version of face painting.

Truncated icosahedron
polyhedron soccer ball
soccer ball

Net truncated icosahedron

The figure shows the net of a truncated icosahedron:
net Truncated  icosahedron

In this case, we did not combine all the details into a single net, because if we print it on a single A4 sheet, the final scale of the assembled figure will be very small.

To build a model, you can download a net in pdf format and print on two A4 sheets. Please note that the sheets are the same!

The scan is made in the colors corresponding to the classic coloring of a football.

download net Truncated icosahedron

Video. The process of converting an icosahedron to a truncated icosahedron

The truncation of all 12 vertices of the icosahedron leads to the formation of a truncated icosahedron. The triangular faces of the original polyhedron lose their area and are converted to hexagonal faces.

Video. Build a polyhedron from a single net

This video from our partners, the ART KOSEKOMA team, clearly demonstrates how the pattern is converted into a geometric shape:

 

Truncated icosahedron from the set "Magic Edges"

archimedean solids magic edges
To assemble polyhedra, we can offer you ready-made patterns that are cut and folded.
To do this, you need to use the details of the set Magic Edges 19.
Also, in the release itself, you will find information about the structure of the polyhedron.
 
Polyhedra, from the set Magic Edges 19:
 
Assembling a truncated icosahedron from the set "Magic Edges"
 
Detailed assembly from Alexei Zhigulev (youtube channel - Origami)
 

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