Page 213 - ICSE Math 7

Let’s find Faces (F), vertices (V) and edges (E) for the following solids.

Cube:
Vertex
• Vertices: The 8 corners of a cube are its vertices.
• Edges: A cube has 12 edges as shown in the adjoining figure. Face
Edge
• Faces: The 6 flat surfaces that form a cube are called its faces.
Cuboid:

• Vertices: The 8 corners of a cuboid are its vertices.
• Edges: Cuboid has 12 edges as shown in the adjoining figure. Edge
• Faces: The 6 flat surfaces that form a cuboid are called its faces. Face

Now let’s find the vertices, edges and faces of a pyramid and a cone.
Vertex

Pyramid: Cone: Vertex
A triangular pyramid as shown has: A cone has:

• 4 vertices Vertex • one vertex Curved
• 6 edges • one curved edge surface
• 4 faces Edge • one curved surface
Face
and one flat face Flat face Curved edge

We can clearly see that the faces of 3D objects are 2D figures. For example, a cube has six faces which
are squares. A triangular pyramid has triangles as its faces. A cone has a circle as its face.

If, F, E and V represent the faces, edges and vertices of a polyhedron (prism or pyramid) respectively
then F + V – E = 2. This is known as Euler’s formula.
The number of vertices (V), number of faces (F) and the number of edges (E) of some 3D figures are
given in the table.

Number of Number of Number of
S. No. Figure
Vertices (V ) Faces (F ) Edges (E)

1. 8 6 12

Cuboid

2. 8 6 12

Cube

3. 1 2 1

Cone

199