Relation between number 0-faces and 1-faces of simple polytope

Question

I want to prove the following:

$d*f_{0}(P)=2*f_{1}(P)$

where P is a d-dimensional convex simple polytope in $R^{d}$ and $f_{0}(P)$ denotes the number of vertices of P and $f_{1}(P)$ the number of edges of P. A d-dimensional polytope P is simple, if every vertex is contained in exactly d facets of P.

Answer 1

Every vertex of a simple $d$-polytope is incident to $d$ edges.

So the total number of vertex-edge incidences is $d \cdot f_0(P)$.

Every edge is incident to 2 vertices.

So the total number of vertex-edge incidences is $2 \cdot f_1(P)$.