Topology: Euler Characteristic

Explore χ = V − E + F across polyhedra and surfaces

Choose a Polyhedron

Euler Characteristic
2
V − E + F = 4 − 6 + 4 = 4
Genus 0 (Sphere-like)
4
Vertices
6
Edges
4
Faces
Euler's Theorem: For any convex polyhedron, V − E + F = 2. This topological invariant only changes when the surface's genus (number of holes) changes.

Sphere: χ = 2   Torus: χ = 0
Double Torus: χ = −2