Why is the euler characteristic of the sphere not 1

[CarrotFish1024]

The same as the title.

 

[HallsofIvy]

What?? Why should it be? The Euler characteristic is a topological invariant so the Euler characteristic of a sphere is the same as the Euler characteristic of a cube: 4 vertices- 12 edges+ 6 faces= 2.

 

[Dr.Peterson]

Why is the euler characteristic of the sphere not 1

The same as the title.

You'll have to explain why you think it should be 1. Very likely you calculated it using an improper network on the sphere.

The reason it can't be 1 is that it is 2. The answer to your underlying question requires seeing your thinking so we can correct it.