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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.
Answers (1)
| 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 |
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