Klein Bottle Fundamental Polygon (2D) — Topology Simulator

🌀 Klein Bottle — Fundamental Polygon

A Klein bottle can't be drawn without self-intersection in 3D, but its true 2D definition is a square with edges glued: left↔right straight, top↔bottom flipped (twisted). Click the square to launch a traveler dot.

Speed 1.0× Heading (°) 27°

📍 Live status

Position (u, v)

0.00, 0.00

Edge crossings

Twist flips

Surface

Klein

ℹ️ Identification rule

Exit right → re-enter left at the same height (single-arrow edges, same direction). Exit top → re-enter bottom at the mirrored horizontal position (double-arrow edges, opposite direction) — that flip is the non-orientable twist. A torus glues both pairs straight, with no flip.