Mathematics
The Euler Characteristic and Its Invariance Under Triangulation
Quick fact
The Euler characteristic of any convex polyhedron is always 2, no matter how you subdivide it into triangles. This means a cube, a pyramid, and a soccer ball all have the same 'Euler number,' revealing that this number depends only on the shape's fundamental structure, not its exact form.
Why this is interesting
Take any polyhedron, count its vertices, subtract edges, add faces—you'll always get the same number. But this number isn't just a coincidence; it's a deep secret about the shape's very nature.