Euler's polyhedron formula
For any convex polyhedron: vertices minus edges plus faces equals 2. History: 1750.
How to work it out
- 1
The statement:
- 2
For any convex polyhedron: vertices minus edges plus faces equals 2.
- 3
Below, the numbers in the table are computed by this site from the definition, not copied.
LaTeX source of the formulas on this page
\[ V - E + F = 2 \]
The five regular solids (computed)
| Solid | V | E | F | V ā E + F |
|---|---|---|---|---|
| Tetrahedron | 4 | 6 | 4 | 2 |
| Cube | 8 | 12 | 6 | 2 |
| Octahedron | 6 | 12 | 8 | 2 |
| Dodecahedron | 20 | 30 | 12 | 2 |
| Icosahedron | 12 | 30 | 20 | 2 |
Questions
What is the euler's polyhedron formula?
For any convex polyhedron: vertices minus edges plus faces equals 2.
Who is the Euler's polyhedron formula associated with?
Leonhard Euler.