wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

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

Open in App
Solution


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=N0 is the number of polyhedron vertices, E=N1 is the number of polyhedron edges, and F=N2 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.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon