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  "body": "\n## Summary\n\nThe symmetry group of an object is the group of all transformations of the ambient space that map the object onto itself. These transformations must keep the relevant structure of the object.\nThe operation is composition of transformations.\nIt is often written $\\operatorname{Sym}(X)$ for an object $X$.\n\n## Remarks\n\nThe symmetry group of a regular $n$-gon in the plane is the [[dihedral group|0JZ27DMJ5D]] of order $2n$.\nThe rotations of a regular tetrahedron form a group [[isomorphic|08MG7H8JW5]] to the [[alternating group|0Z5905Q73D]] $A_4$.\nThe symmetry group of an object is a [[subgroup|0X1JXT47GA]] of the group of all transformations of the ambient space.\n\n## Explanations\n\n### L1 human\n\nA symmetry of an object is a motion that leaves the object looking the same.\nTwo symmetries done one after the other give another symmetry, and each symmetry can be undone.\nSo the symmetries of an object form a group, and this group measures how symmetric the object is.\n",
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