What is an Edge, Vertex and a Face?

• A vertex in a geometrical figure can be defined as a corner.
• A line segment between faces is known as an edge.
• A single flat surface is known as face.

What are Vertices?

• A point where two or more line segments meet is known as a vertex.
• The plural of vertex is vertices.
• In simpler words, we can say that a vertex is a corner.
• For example, a tetrahedron has 4 vertices and a pentagon has 5 vertices.

Here’s a List of Shapes along with the Number of Vertices. 

What are Edges?

• An edge in a shape can be defined as a point where two faces meet.
• For example, a tetrahedron has 4 edges and a pentagon has 5 edges.
• The line segments that form the skeleton of the 3D shapes are known as edges.
• For a polygon, we can say that an edge is a line segment on the boundary joining one vertex (corner point) to another.
•  A Tetrahedron Has 6 Edges
• For polyhedron shapes a line segment where two faces meet is known as an edge.

Here’s a List of Shapes along with the Number of Edges.

What do you Mean by Faces?

• A face of a figure can be defined as the individual flat surfaces of a solid object.
• Example, a tetrahedron has 4 faces one of which is not visible.

Here’s a List of Shapes along with the Number of Faces. Faces of 3d Shapes are Given Below:  

Euler’s Formula for Polyhedron:

What is Euler’s Formula for Types of Polyhedron?

• The Euler theorem is known to be one of the most important mathematical theorems named after Leonhard Euler.
•  The theorem states a relation of the number of faces, vertices, and edges of any polyhedron. 
• The Euler’s formula can be written as F + V = E + 2, where F is the equal to the number of faces, V is equal to the number of vertices, and E is equal to the number of edges.
•  The Euler’s formula states that for many solid shapes the number of faces plus the number of vertices minus the number of vertices is equal to 2.

Euler’s Formula:

For example ,

Let us take a cube,

Let’s List Down the Number of Faces, Sides and Vertices.

Let’s apply the Euler’s Formula,

Euler’s Formula:

=6+8-12

= 14-12  = 2

This is how the Euler’s formula works.

Note: The Euler’s formula for polyhedron generally deals with shapes called Polyhedron shapes. 

Now You Might Think What is a Polyhedron?

Here’s what is a polyhedron,

A closed solid shape which has flat faces and straight edges is known as a Polyhedron. There are different types of polyhedron. A cube can be an example of a polyhedron whereas as a cylinder has curved edges it is not a polyhedron. Euler’s formula for polyhedron generally works for types of polyhedrons.

Summary:

Question 3) Show how the Euler’s formula works for a cube.

Solution) 

Let’s List Down the Number of Faces, Sides and Vertices of Polyhedron Shapes.

Let’s apply the Euler’s Formula,

Euler’s Formula:

=6+8-12

= 14-12

= 2