Question

Euler’s formula for any polyhedron, where F stands for the number of faces, V stands for the number of vertices and E stands for the number of edges is
A. $ F+V+E=2 $
B. $ F-V+E=2 $
C. $ F+V-E=2 $
D. $ F-V-E=2 $

Answer 1

Hint: First, we try to find the definition of the polyhedron and find its difference from a regular polygon. Then we take some examples of a polyhedron and try to find the values of $ F,V ,E $ . We put the values in the given options to find the correct option which matches all the polyhedrons.

Complete step by step answer:
A polyhedron is a solid object whose surface is made up of a number of flat faces which themselves are bordered by straight lines. Each face is in fact a polygon, a closed shape in the flat two-dimensional plane made up of points joined by straight lines.
For example tetrahedron, cube, octahedron all are polyhedron. We try to find the values of $ F,V,E $ where F stands for the number of faces, V stands for a number of vertices and E stands for the number of edges.
For tetrahedron, we have $ F=4,V=4,E=6 $ .
For cube, we have $ F=6,V=8,E=12 $ .
For octahedron, we have $ F=8,V=6,E=12 $ .
We find the value of $ F+V-E $ for all three polyhedrons. $ F+V-E=2 $ .
All other options don’t match the polyhedrons.
The correct option is C.

Note:
 Euler’s formula can be used to investigate what properties an individual object can have and to identify properties that all of the must-have. Euler's formula can tell us, for example, that there is no simple polyhedron with exactly seven edges.