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A specific set of graphs was given here:

Let $G$ be a 3-regular connected planar graph with a planar embedding where each face has degree either 4 or 6 and each vertex is incident with exactly one face of degree 4. Determine the number of vertices, edges and faces of degree 4 and 6.

For following set of equations was given as answer:

  1. $2E=3n$
  2. $2E=4F_4+6F_6$
  3. $n-E+F_4+F_6=2$
  4. $n=4F_4$

For bicubic planar graphs consisting of $4$- and $6$-faces only, $F_4=6$ (see here), so $n=4\cdot 6=24$ then $E=36$ and finally $F=14$. How does such a graph look?

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Ah I found it: Truncated octahedron;

enter image description here

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