Is the Euler's polyhedron formula valid for cylinders?

Question

Can cylinders be considered as polyhedrons for applying the Euler's formula, V-E+F=2 (V: vertices, E: edges, F: faces)? If so, what are the values of V, E and F?

Answer 1

actually eulers equation is a special case of a more general equation
V-E+F = X : X= 2-2g

g is the genus of the figure. for cylinders x=0
(cylinder is not a closed polyhedra for all closed polyhedras euler equation is valid, so for spheres , tetrahedrons the euler equation works)

so v-e+f = 0 no vertices two faces (inside ,outside) and two edges fit the equation 0-2+2 = 0

for a sphere one vertex hastobe assumed as it is impossible to construct a sphere (closed) without taking one reference point , and one face gives 1-0+1 = 2 ; normal euler equation

THE GENUS : please goto mathworld.com website for a definition

Answer 2

Euler Polyhedron Formula

Answer 3

I think it might be V=2, E = 1 and F =1 . Imagine that you stretch the cilinder and you obtain a rectangular.
ABCD where the vertex A is "identified" with B, the vertex C is "identified with" D, so the side AC is "identified" with BD.
So there are 2 vertices, one edge AC and one face ABCD.
Anyhow I don't guarantee the proof( though such procedures are used in algebraic topology).


But at wikipedia you finf the formula for Euler characteristic:
The Euler characteristic of a closed orientable surface can be calculated from its genus g (the number of tori in a connected sum decomposition of the surface; intuitively, the number of "handles") as
χ = 2 − 2g.

Now the cilinder is a orientable surface and its number of "handles" is 0, so X = 2 - 0 = 2 (not surprising)

I need to read more algebraic toplogy.

Answer 4

For a convex polyhedron, V - E + F = 2 1) 7 - E +7 = 2, E = 12 2) V - 30 + 12 = 2, V = 20 3) 12 - 18 + F = 2, F = 8

Answer 5

It doesn´t make any sens because a cilinder
has NO vertices ,edges .It is NOT a polyhedron