Tabulate the number of faces, edges and vertices for the following polyhedrons: (Here ‘V’ stands for number of vertices, ‘F’ stands for number of faces and ‘E’ stands for number of edges).
Solid | F | V | E | F+V | E+2 |
---|---|---|---|---|---|
Cuboid | |||||
Triangular pyramid | |||||
Triangular prism | |||||
Pyramid with square base | |||||
Prism with square base |
What do you infer from the last two columns? In each case, do you find
, i.e., ? This relationship is called Euler’s formula.
In fact this formula is true for any polyhedron.
Solid | F | V | E | F+V | E+2 |
---|---|---|---|---|---|
Cuboid | 6 | 8 | 12 | 14 | 14 |
Triangular pyramid | 4 | 4 | 6 | 8 | 8 |
Triangular prism | 5 | 6 | 9 | 11 | 11 |
Pyramid with square base | 5 | 5 | 8 | 10 | 10 |
Prism with square base | 6 | 8 | 12 | 14 | 14 |