A tetrahedron is a polyhedron with four faces.
Tetrahedron is a concept that is used in the field of geometry . To understand what the term refers to, whose etymological origin is in the Greek language, it is important to know the meaning of polyhedron : a solid body of finite volume that has flat faces.
With this clear, we can move forward with the definition of a tetrahedron. It is a polyhedron that has four faces . These data imply that tetrahedra are convex polyhedra , since all the segments that link two of their points are located within the polyhedron.
Characteristics of a tetrahedron
The properties of the tetrahedron make its faces, on the other hand, triangular . At each vertex , in this way, three of the faces meet. When all of these faces are equilateral triangles (that is, triangles that have three equal sides), the tetrahedron is classified as regular . In other words: a regular tetrahedron is a tetrahedron that has four equilateral triangles as faces.
In every tetrahedron, the segments that link the vertices with the intersection points that belong to the medians of the opposite face are concurrent at a point . Similarly, the midpoints of the pairs of opposite edges are also concurrent at the same point.
Another peculiarity of tetrahedra is that the planes perpendicular to the edges according to their midpoints cross the same point , while the lines perpendicular to their circumcenter to the faces are concurrent in the center of the sphere that is circumscribed to the polyhedron in question. .
Tetrahedra can be used in different ways.
The symmetry
Symmetry is one of the particular properties of the tetrahedron, as explained below. The number of axes of axial symmetry of a regular tetrahedron is four, and all are of rotation order three. It should be remembered that an axis of axial symmetry is a line around which a figure can rotate without its visual appearance being altered; Regarding the order of rotation , it is the number of times we must rotate the smallest angle to complete a turn, that is, to reach 360°.
With respect to the plane axes of symmetry , that is, a line that divides any geometric shape into two parts, in such a way that the opposite points are at equal distance from it, the tetrahedron has six, and they are those that are formed between each edge and the midpoint of its opposite.
Other properties of the tetrahedron
We also have conjugation , a property of the regular tetrahedron that proposes it as the only "self-conjugated" Platonic solid, that is, conjugated to itself, and this can be verified with the equation b = a / 4 , where a is the edge of a tetrahedron and b represents the one we obtain by conjugating it.
To understand another of the particular properties of the tetrahedron, it is necessary to explain the concept of orthogonal projection , which is achieved by drawing lines perpendicular to the plane in which it is made, regardless of the angle of the projected figure. In the case of regular tetrahedra, applying this type of projection can give us one of two figures:
* a triangle : this occurs if one of its faces is parallel to the plane of projection, since the other three (which are also triangles) cannot be perceived from the point of view of the plane, which will simply collect the three extreme points of the tetrahedron , which in this case are three vertices of one of its triangles ;
* a quadrilateral : when two opposite edges of the original figure are parallel to the plane of projection, then we obtain a square as a result, whose side is equivalent to dividing the length of the edge by the square root of two.