I was wondering if there's any formula to calculate the number of edges and vertices of a polyhedrons? like Dodecahedron, Icosahedrons, (or generally for polyhedrons with a certain number of faces)
The number of faces is not enough to determine the number of edges and vertices. However, we have Euler's formula
Euler's Formula
Simple example I came up with on paper to illustrate how # faces does not uniquely determine # edges and # vertices.
1) square pyramid
2) a wedge you'd use to hold a door open
Both have five faces but number of edges and vertices are different.