In Geometry, a 3D object having width, height and depth is referred to as a solid object. 3D solid objects have 3 important attributes: these are called as faces, vertices and edges. For example, let us take a 3D object as shown below:


Definition of face
As you can see from the above diagram, the flat surface of the 3D solid is called as the face. The edge is the line where two faces meet and the vertex is the point at which two or more edges meet.

Faces can be of different shapes. For example circle, square, rectangle, polygon and so on depending on the 3D object. Also a face can be a flat surface or a curved surface. Let us take a look at some examples of 3D solid objects and see the number and types of faces that they have.

A triangular pyramid like the one shown in the figure above has 4 triangular faces. These are all flat faces.

A cube has 6 flat square faces. A cuboid has 6 faces out of which 2 are square faces and 4 are rectangular faces. They are all flat faces.

A cylinder has 2 flat circular faces and one curved face. Similarly, a cone has one flat circular face and one curved face.

Related terms
A 3D solid object that is only bound by flat faces is known as a polyhedron.

Euler’s formula:

You will find that for many solid objects, the number of faces plus the number of vertices minus the number of edges is equal to 2.

Take the example of a cube where number of faces is equal to 6, number of vertices is equal to 8 and number of edges is equal to 12
Hence, replacing the numbers in the above equation we get 6 + 8 - 12 = 2.

You can easily study faces by using objects around you. A pencil box is a good example of a cuboid, so is also a duster. You can use a battery cell as a cylinder and count the number of flat and curved faces. A dice is a cube with 6 flat faces. Sometimes faces are given further names. For example, if we hold a cylinder erect then we have a top face and bottom face as shown in the figure below:



Download Free Faces in Geometry Formula PDF:



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