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  "body": "\n## Summary\n\nAn orbifold is a space that looks near each point like the quotient of an open subset of $\\R^n$ by a finite group.\nIt generalizes a [[smooth manifold|R2TQ82PCNB]], which is the case where all these groups are trivial.\nOrbifolds arise as quotients of manifolds by properly discontinuous actions of discrete groups, which may have fixed points.\nThey are central in the geometry of surfaces and $3$-manifolds.\n\n## Explanations\n\n### L1 human\n\nFold a sheet of paper into a cone: near the tip the cone is not flat, but it still looks like a flat disk divided by a rotation.\nAn orbifold is a space built from such pieces, where each piece is a flat piece of $\\R^n$ divided by a finite group of symmetries.\nFor example, rotate the plane $\\R^2$ by a third of a turn around the origin.\nPoints that are moved into each other are glued, and the result is a cone with one special point, the image of the origin.\nThe cone point remembers that the group of order $3$ fixed it.\n",
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