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🌀 Klein Bottle Fundamental Polygon (2D)

Interactive 2D fundamental-polygon model of the Klein bottle: a square whose edges are glued with a twist. Watch a traveler dot cross the edges and reappear per the real identification rule, and compare against the untwisted torus gluing.

Mathematics2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

⚙ Under the hood

The 2D fundamental-polygon model of the Klein bottle: a square whose left and right edges glue straight while its top and bottom edges glue with a twist. Launch a traveler dot to watch it wrap through the real edge identifications, count its crossings and flips, and compare against an untwisted torus gluing.

klein bottlefundamental polygontopologynon-orientable surfaceedge identificationtorus

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