Translation and analysis of words by ChatGPT artificial intelligence
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tetrahedral group - translation to russian
![volleyball]] have pyritohedral symmetry](https://commons.wikimedia.org/wiki/Special:FilePath/Volleyball seams diagram.png?width=200 "volleyball]] have pyritohedral symmetry")
общая лексика
группа тетраэдра
![Ga2Cl6}} ("[[gallium trichloride]]").](https://commons.wikimedia.org/wiki/Special:FilePath/Gallium-trichloride-from-xtal-2004-3D-balls.png?width=200 "Ga2Cl6}} (\"[[gallium trichloride]]\").")
![<!-- specify width as minus sign vanishes at most sizes --> Calculating bond angles of a symmetrical tetrahedral molecule using a [[dot product]]](https://commons.wikimedia.org/wiki/Special:FilePath/Tetrahedral angle calculation.svg?width=200 "<!-- specify width as minus sign vanishes at most sizes --> Calculating bond angles of a symmetrical tetrahedral molecule using a [[dot product]]")
математика
тетраэдальный комплекс (прямых)
математика
групповая операция
Wikipedia
A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.
The group of all (not necessarily orientation preserving) symmetries is isomorphic to the group S4, the symmetric group of permutations of four objects, since there is exactly one such symmetry for each permutation of the vertices of the tetrahedron. The set of orientation-preserving symmetries forms a group referred to as the alternating subgroup A4 of S4.
