Shapes that have the same Euler Characteristic could be turned into each other by the right set of manipulations, whereas those that have a different Euler Characteristic cannot?
I'm after a short, simple but correct explanation for children ~10 years old of why the Euler Characteristic is a 'basic idea in topology' (as I've read). It's for use as a 'by the way, you might be interested to know...' insight into more advanced maths to conclude an exercise of counting faces, vertices and edges of common 3D shapes, and discovering that they usually have an Euler Characteristic of 2 (The only exception I've been able to think of among common 3D shapes is a cylinder, which I think has 3 faces, 0 vertices and 2 edges, so an Euler Characteristic of 1.).
Thanks for your help!