Page 203 - ICSE Math 8

(b) Quadrilateral Pyramid: If the base of a pyramid is a quadrilateral, it is V
called a quadrilateral pyramid (Fig. 18.20). If the quadrilateral is in the
form of a square, it is a square pyramid. If the quadrilateral is in the form
of a rectangle, it is a rectangular pyramid. It has:
(i) 5 vertices and 8 edges C
(ii) 4 triangular lateral faces D
Similarly, a pyramid is named as pentagonal, hexagonal, heptagonal, O
octagonal and so on based on the number of sides being five, six, seven, A
eight and so on respectively. Fig. 18.20 B

Platonic Solids

The regular, convex polyhedra (plural of polyhedron) are known as the platonic solids. There are only five
platonic solids. In a platonic solid,
(i) at least three faces meet at a vertex to form a solid angle.
(ii) the sum of all plane angles forming the solid angle at a vertex is less than 360º.
The following table shows how the Euler’s formula applies to platonic solids:

Name of platonic Number of Number of Number of
solid faces (F) vertices (V) edges (E)

Tetrahedron

4 4 6

Hexahedron (Cube)

6 8 12

Octahedron

8 6 12

Icosahedron

20 12 30

Dodecahedron

12 20 30

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