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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.
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. 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.
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.
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.
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