Dodecahedrons are three-dimensional figures formed by 12 pentagonal faces. Dodecahedrons are one of the five platonic solids. In total, dodecahedrons have 12 faces, 30 edges, and 20 vertices. Three pentagonal faces meet at each vertex.
In this article, we will learn about the faces, vertices, and edges of dodecahedrons in more detail.
Faces of a dodecahedron
The faces of dodecahedrons are the two-dimensional flat surfaces that form the three-dimensional dodecahedron. Dodecahedrons have a total of twelve pentagonal faces.
Another way to define the faces of the dodecahedrons is as the two-dimensional pentagons that are formed by the vertices and the edges.
Each face of the dodecahedron connects with five other pentagonal faces.
Since dodecahedrons are regular figures, their twelve faces have the same shape and the same dimensions. Therefore, all twelve faces of the dodecahedron are congruent.
This means that to calculate the surface area of a dodecahedron, we have to find the area of one of the faces and multiply by 12. Thus, we have:
$latex A_{s}=12A_{p}$
where, $latex A_{p}$ is the area of one of the pentagonal faces of the dodecahedron.
Alternatively, we can use the standard formula for the Surface Area of a Dodecahedron:
$$A_{s}=3\sqrt{25+10\sqrt{5}}~{{a}^2}$$
Vertices of a dodecahedron
The vertices of a dodecahedron are the points where the edges meet. Specifically, three edges meet at each vertex of a dodecahedron.
Alternatively, we can also define the vertices of a dodecahedron as the points where three pentagonal faces of the dodecahedron meet.
In total, we have 20 vertices in dodecahedrons. Since the faces are pentagonal, each face is made up of 5 vertices and each vertex is shared by three faces.
Edges of a dodecahedron
The edges of a dodecahedron can be defined as the line segments joining two vertices. The edges form the outline of each pentagonal face of an octahedron.
Another way to define edges is as the line segments where two pentagonal faces of the dodecahedron meet. Therefore, we know that the edges lie on the limits of the dodecahedron.
In total, dodecahedrons have 30 edges. Since the faces are pentagonal, each face of the dodecahedron has five edges, as we see in the diagram below.
In the diagram, we see that each face of the dodecahedron has five edges, and each edge is shared by another face.
See also
Interested in learning more about dodecahedrons? Take a look at these pages:
Jefferson Huera Guzman
Jefferson is the lead author and administrator of Neurochispas.com. The interactive Mathematics and Physics content that I have created has helped many students.
