3-Topology-Topologies

Klein bottle

One-sided-surface bottles {Klein's bottle} {Klein bottle} have genus one, because it has one handle.

Mobius strip

One-sided surfaces {Möbius strip}| {Möbius band} can exist. Normal that moves around surface axis from point and returns to the point has opposite direction. If it goes around again, it has original direction.

polyhedron in topology

Two-dimensional-polygon sets {polyhedron, topology} can change into triangles, or triangle sets can change into polygons.

compact space in topology

Two-dimensional spaces {compact space} can be planes, spheres, or saddles.

Thurston conjecture

Three-dimensional compact spaces have eight basic shapes {Thurston conjecture} (William Thurston) [1985].

wallpaper group

Plane has 17 figure symmetries {wallpaper group, topology}.

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3-Topology

Drawings

Drawings

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Date Modified: 2022.0225