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2. Rectangular Pyramid: A rectangular pyramid has 5 vertices, 8
edges and 5 faces – 4 of its lateral faces are triangular and 1 is Triangular
rectangular base. If the base is a square, then it is a square lateral face
pyramid.
3. Pentagonal Pyramid: A pentagonal pyramid has 6 vertices, 10
edges and 6 faces–5 of its lateral faces are triangular and 1 is pentagonal
base. Triangular
lateral face

If the base of a pyramid is a polygon of n sides then it has n lateral faces, (n + 1) vertices and 2n
Note: edges. For example, if the base is a hexagon, then it is a hexagonal pyramid. It has 7 vertices, 12
edges and 7 faces.

Regular Polyhedron (Platonic Solids)

If a polyhedron has faces made up of congruent regular polygons and
that the same number of faces meet at each vertex, then it is known Remember
as a regular polyhedron. Regular convex polyhedrons are also called Solid angle is an angle made
Platonic Solids. It has: by three or more planes
1. All the faces are regular and congruent. joining at a common point.
2. At least three faces meet at a vertex to form a solid angle.
3. All plane angles together forming the solid angle at the vertex is less than 360°.
Read different types of platonic solids.

1. Tetrahedron: It is a triangular pyramid. Its faces are congruent equilateral triangles.
2. Hexahedron: It is a polyhedron with 6 square faces, 12
edges and 8 vertices. It is commonly known as a cube.
3. Octahedron: It is a polyhedron with 8 faces, 12 edges and
6 vertices with 4 equilateral triangles meeting at each
vertex.
4. Icosahedron: It is a polyhedron with 20 faces, 30 edges
and 12 vertices with 5 equilateral triangles meeting at
each vertex.
5. Dodecahedron: It is a polyhedron with 12 faces, 30 edges
and 20 vertices with 3 pentagons meeting at each vertex.
Euler’s Formula

The Euler’s formula states that the number of faces (F), number of vertices (V) and the number of
edges (E) in a simple convex polyhedron has a certain relation, which is as follows:

F + V – E = 2
The following table shows the number of faces, vertices and edges of some platonic solids.
Name of Platonic Solids Numbers of Faces (F) Numbers of Vertices (V) Number of Edges (E)
Tetrahedron 4 4 6
Hexahedron 6 8 12
Octahedron 8 6 12
Icosahedron 20 12 30
Dodecahedron 12 20 30

223 Visualising Solid Shapes