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📐 Fundamental Polygon Genus Explorer (2D)

Interactive 2D fundamental-polygon representation of genus-g surfaces. Watch a 4g-sided polygon with edge identifications aba⁻¹b⁻¹... represent a sphere, torus, double torus and beyond, with a live loop that wraps through the edge gluing and the Euler characteristic χ = 2 − 2g updating in real time.

Mathematics2DAdvanced60 FPS📱 Mobile-adapted⇄ 3D version

⚙ Under the hood

Explore genus-g surfaces through their fundamental polygon: a 4g-sided polygon with edges glued in the pattern a1b1a1⁻¹b1⁻¹… represents a sphere, torus, double torus, and beyond. Watch a loop travel through the identified edges and reappear on its glued partner, while the Euler characteristic χ = 2 − 2g updates live.

topologygenusfundamental polygonEuler characteristicmath2D

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install