WHAT IS THE EDGE OF A CUBE? - MATHS - 2024

The edge of a cube is an edge of the same: it is the line that joins two vertices or corners. An edge is the line where two faces of a geometric figure intersect.

The above definition is general and applies to any geometric figure, not just the cube. When it is a flat figure, the edges correspond to the sides of said figure.

A geometric figure with six faces in the form of parallelograms is called parallelepiped, of which the opposite ones are equal and parallel.

In the particular case in which the faces are square, the parallelepiped is called a cube or hexahedron, a figure that is considered a regular polyhedron.

Ways to identify the edges of a cube

For better illustration, everyday objects can be used to determine precisely what the edges of a cube are.

1- Assembling a paper cube

If you look at how a paper or cardboard cube is built, you can see what its edges are. It begins by drawing a cross like the one in the figure and certain lines are marked inside.

Each of the yellow lines represents a fold, which will be an edge of the cube (edge).

Similarly, each pair of lines that have the same color will form an edge when joined. In total, a cube has 12 edges.

2- Drawing a cube

Another way to see what the edges of a cube are is to see how it is drawn. We begin by drawing a square with side L; each side of the square is an edge of the cube.

Then four vertical lines are drawn from each vertex, and the length of each of these lines is L. Each line is also an edge of the cube.

Finally, another square with side L is drawn, such that its vertices coincide with the end of the edges drawn in the previous step. Each of the sides of this new square is an edge of the cube.

3- Rubik's cube

To illustrate the geometric definition given at the beginning, you can look at a Rubik's cube.

Each face has a different color. The edges are represented by the line where faces with different colors intersect.

Euler's theorem

Euler's theorem for polyhedra says that given a polyhedron, the number of faces C plus the number of vertices V equals the number of edges A plus 2. That is, C + V = A + 2.

In the previous images you can see that a cube has 6 faces, 8 vertices and 12 edges. Therefore, it fulfills Euler's theorem for polyhedra, since 6 + 8 = 12 + 2.

Knowing the length of an edge of a cube is very useful. If the length of an edge is known, then the length of all its edges is known, with which certain data about the cube can be obtained, such as its volume.

The volume of a cube is defined as L³, where L is the length of its edges. Therefore, to know the volume of the cube it is only necessary to know the value of L.

References

1. Guibert, A., Lebeaume, J., & Mousset, R. (1993). Geometric activities for Infant and Primary Education: for infant and primary education. Narcea Editions.
2. Itzcovich, H. (2002). The study of figures and geometric bodies: activities for the first years of schooling. Noveduc Books.
3. Rendon, A. (2004). ACTIVITIES NOTEBOOK 3 2nd HIGH SCHOOL. Editorial Tebar.
4. Schmidt, R. (1993). Descriptive geometry with stereoscopic figures. Reverte.
5. Spectrum (Ed.). (2013). Geometry, Grade 5. Carson-Dellosa Publishing.