Concepts related to polyhedron

1. Polyhedron
A polyhedron is a three-dimensional solid made up of
polygons. It has flat faces, straight edges, and vertices.
For example, a cube, prism, or pyramid are polyhedrons.

2. Parts of a Polyhedron
The dimensions of a polyhedron are classified as faces, edges,
and vertices.
Face: The flat surface of a polyhedron is termed as its face.
Edge: The two faces meet at a line called the edge.
Vertices: The point of intersection of two edges is a vertex.

4. Euler’s formula:F+V=E+2 Or F+V-E=2

5. Ws-8
• 1. How many faces do the following polyhedrons have?
• (i) Triangular prism (ii) Rectangular pyramid (iii) Triangular pyramid
• Ans : Triangular prism-5 (ii) Rectangular pyramid-5 (iii) Triangular pyramid-4
• 2. How many vertices and edges do the following polyhedrons have?
• (i) Square pyramid (ii) Triangular prism
• Answer 2.Square pyramid –V-5,E-8
• (ii) Triangular prism:-V-6,E-9

6. 3 Is a Square prism same as a cube? Explain
Answer 3:No, square prism is not a cube because lateral faces of cube square but in square
prism lateral faces are rectangular.
4. Verify Euler’s formula for the given figures.
Answer 4:

7. 5. Using Euler’s formula, find the unknown.
6. Can a polyhedron have 10
faces, 20 edges and 15
vertices?