A tetrahedron is a three-dimensional figure, which consists of only triangular faces. These geometric shapes are one of the five Platonic solids. Tetrahedra have 4 faces, 6 edges, and 4 vertices. Three faces of the tetrahedron meet at each vertex.

Here, we will learn about the faces, vertices, and edges of tetrahedra in more detail. We will learn about these parts using diagrams.

GEOMETRY
Vertices of a tetrahedron

Relevant for

Learning about the faces, vertices, and edges of tetrahedra.

See faces

GEOMETRY
Vertices of a tetrahedron

Relevant for

Learning about the faces, vertices, and edges of tetrahedra.

See faces

Faces of a tetrahedron

The faces of a tetrahedron are the flat surfaces that give it its three-dimensional shape. Those faces are formed by the vertices and the edges. All faces of a regular tetrahedron are equilateral triangles.

Since tetrahedra can be considered triangular pyramids, one of the faces is the base and the other three are lateral faces. That is, a tetrahedron has four triangular faces in total.

The three lateral faces of the tetrahedron meet at a single point, located in the upper part, that can be considered the main vertex.

Faces of a tetrahedron

We can calculate the surface area of a tetrahedron by adding the areas of the four triangular faces. In the case of a regular tetrahedron, we know that all four faces are equal, so we have:

A_{s}=4A_{t}

where, A_{t} is the area of one of the triangular faces.

Alternatively, we can calculate the surface area of a regular tetrahedron, using the standard formula:

A_{s}=\sqrt{3}{{a}^2}


Vertices of a tetrahedron

In general terms, vertices can be thought of as the points where two or more line segments meet. In the case of tetrahedrons, the vertices are the points where three edges meet.

Alternatively, we can also think of the vertices of a tetrahedron as the points where three faces meet. In total, tetrahedra have 4 vertices.

The upper vertex where three lateral faces meet can be considered the main vertex of the tetrahedron.

Vertices of a tetrahedron

Edges of a tetrahedron

In general terms, we can consider the edges as the line segments that join two vertices. In total, a tetrahedron has 6 edges.

We can also define edges as the line segments where two triangular faces of the tetrahedron meet. The edges are located at the limits of the tetrahedron.

In the diagram, we can see that each face of the tetrahedron has three edges and each edge is shared by two triangular faces.

Edges of a tetrahedron

See also

Interested in learning more about tetrahedra? Look at these pages:

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