📐 Fundamental Polygon — Genus Explorer (2D)
4g-gon with edge identification a₁b₁a₁⁻¹b₁⁻¹…
🔗 3D version
Genus g
g =
0
0–4
χ = 2
Genus g
0
χ = 2 − 2g
2
Polygon sides (4g)
0
π₁ generators
0
Display
Edge labels
Animate loop
Fundamental word
trivial (S²)
What you're seeing
Sphere: simply-connected disc, no edge gluing needed. Every loop on it contracts to a point.