Question

Comprehend Euler's polyhedron formula. Also, send in its proof.

Answer 1

Eulers formulae relates the number of polyhedron vertices , faces , and polyhedron edges of a simply connected polyhedron (or polygon). It was discovered independently by Euler (1752) and Descartes, so it is also known as the Descartes-Euler polyhedral formula. The formula also holds for some, but not all, non-convex polyhedra.
The polyhedral formula states
V + F - E = 2,
where $V=N_0$ is the number of polyhedron vertices, $E=N_1$ is the number of polyhedron edges, and $F=N_2$ is the number of faces
Proof
Let G| be a planar graph with V |vertices and E edges.
Let V =1|.
The number of faces F| is then given by:
F = E + 1|
Hence:
V − E + F = 1 − E + ( E + 1 ) = 2 and the formula holds.