The number of vertices relates to the edges and faces of a polyhedron through Euler's polyhedron formula. According to the provided reference, the number of vertices is 2 more than the excess of the number of edges over the number of faces. This relationship is mathematically expressed in Euler's formula.
For example, a cube has 12 edges and 6 faces. Applying this to Euler's formula implies the cube has 8 vertices, since 12 - 6 + 2 = 8.
Here's a breakdown of the formula:
- Let V = Number of Vertices
- Let E = Number of Edges
- Let F = Number of Faces
Then, Euler's formula is: V = E - F + 2
Let's put this into a table for better visualization:
| Polyhedron | Number of Edges (E) | Number of Faces (F) | Calculation (E - F + 2) | Number of Vertices (V) |
|---|---|---|---|---|
| Cube | 12 | 6 | 12 - 6 + 2 | 8 |
