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  "body": "\n## Definition\n\nLet a [[group|G5S1M9]] $G$ [[act|0WCY42EV9V]] on a set $X$, and let $x \\in X$.\nThe orbit of $x$ is the set $G \\cdot x = \\{g \\cdot x : g \\in G\\}$.\nThe set of all orbits is written $X/G$.\n\n## Remarks\n\nThe point $x$ lies in its own orbit, because $e \\cdot x = x$.\nThe [[orbits partition|0ZC7FYE0NZ]] the set $X$.\nFor the action of the rotation group of a square on its corners, there is one orbit, which contains all four corners.\n\n## Explanations\n\n### L1 human\n\nThe orbit of a point collects all the places where the group can move the point.\nTwo points in the same orbit can be moved onto each other.\nPoints in different orbits are never moved onto each other.\n",
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