One-sided-surface bottles {Klein's bottle} {Klein bottle} have genus one, because it has one handle.
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.
Two-dimensional-polygon sets {polyhedron, topology} can change into triangles, or triangle sets can change into polygons.
Two-dimensional spaces {compact space} can be planes, spheres, or saddles.
Three-dimensional compact spaces have eight basic shapes {Thurston conjecture} (William Thurston) [1985].
Plane has 17 figure symmetries {wallpaper group, topology}.
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Date Modified: 2022.0225