Develop spatial imagination

0.00 $
0 item(s)

Truncated tetrahedron. How to make pdf template

This polyhedron is obtained by successively cutting off each of the vertices of the tetrahedron.

A truncated tetrahedron is a semiregular convex polyhedron with two properties:
1. All faces are regular polygons of two types, a hexagon, and a triangle;
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.

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

Archimedean solids are semiregular polyhedra in the sense that their faces are regular non-similar polygons. Simultaneously, the condition of one of the types of spatial symmetry (tetrahedral, octahedral, or icosahedral) is preserved.

Mathematical Characteristics of the Truncated Tetrahedron

A truncated tetrahedron can be placed in a sphere (inscribed) so that each of its vertices touches the sphere's inner wall.

The radius of the described sphere of the Truncated tetrahedron

Where a is the length of the side.

It is impossible to place the sphere inside the Truncated tetrahedron so that it touches all sides simultaneously.
To fulfill this condition, the sphere must touch all squares and triangles.
The distances from the center of the sphere to the middle of the triangles and the middle of the hexagons are different.

The surface area of the Truncated tetrahedron.

The following formula can determine the surface area:

The following formula determines the volume of the Truncated tetrahedron:

A truncated tetrahedron can be represented as a group of regular polyhedra. The figure shows that the truncated tetrahedron can be divided into four octahedra and six tetrahedrons.

Accordingly, it is possible to carry out the opposite operation - in the presence of four octahedra and six tetrahedrons, assemble a truncated tetrahedron model from parts.

Truncated tetrahedron shape nets

The figure shows the shape net of a truncated tetrahedron:

To build a model, you can download the pattern pdf format pattern and print it on an A4 sheet.
If you intend to print it on a color printer, download the color net.

If you intend to use colored paper, use this net.

Also, there are other options for coloring the polyhedron, when each of the neighboring faces is painted in its own color. Or a certain number of coloring colors is used, and the same colors do not border each other.

We present to your attention two options for coloring the truncated tetrahedron.

The first option is a five-color painting. The faces formed by the tetrahedron have different colors, and the faces formed by cutting off the corners of the tetrahedron are painted in the same color:

download the truncated tetrahedron shape net

The second option is a four-color painting. Opposite faces have the same color:

download the truncated tetrahedron shape net

Video. The process of converting a tetrahedron to a truncated tetrahedron

Video. Build a polyhedron from a net

Truncated tetrahedron from the set "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 18.
Also, in the release itself, you will find information about the structure of the polyhedron.

Polyhedra, from the set Magic Edges 18:

Assembling a truncated tetrahedron from the set "Magic Edges"

The rotation of the finished polyhedron assembled from these parts:

Detailed assembly from Alexei Zhigulev (youtube channel - Origami)

Truncated tetrahedron. How to make pdf template

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

Mathematical Characteristics of the Truncated Tetrahedron

Popular