Tetrahedral symmetry
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 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.
332 symmetryAchiral tetrahedral symmetryAlternating groupArchimedean solidBilunabirotundaBinary icosahedral groupBinary tetrahedral groupBring radicalChamfer (geometry)Chiral tetrahedral symmetryCompound of five cubesCompound of five cuboctahedraCompound of five cubohemioctahedraCompound of five great cubicuboctahedraCompound of five great dodecahedraCompound of five great icosahedraCompound of five great rhombihexahedraCompound of five icosahedraCompound of five nonconvex great rhombicuboctahedraCompound of five octahedraCompound of five octahemioctahedraCompound of five rhombicuboctahedraCompound of five small cubicuboctahedraCompound of five small rhombihexahedraCompound of five small stellated dodecahedraCompound of five stellated truncated hexahedraCompound of five tetrahedraCompound of five tetrahemihexahedraCompound of five truncated cubesCompound of five truncated tetrahedraCompound of four octahedra with rotational freedomCompound of six tetrahedra with rotational freedomCompound of ten tetrahedraCompound of ten truncated tetrahedraCompound of two great dodecahedraCompound of two great icosahedraCompound of two icosahedraCompound of two small stellated dodecahedraCompound of two truncated tetrahedraCovering groups of the alternating and symmetric groups
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Symmetry Group
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Tetrahedral symmetry
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 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.
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A regular tetrahedron has 12 r ...... alternating subgroup A4 of S4.
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Die Tetraedergruppe ist die Gr ...... Drehspiegelung unterschieden.
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Правильный тетраэдр имеет 12 в ...... енной подгруппой A4 группы S4.
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title
Tetrahedral group
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TetrahedralGroup
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A regular tetrahedron has 12 r ...... alternating subgroup A4 of S4.
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Die Tetraedergruppe ist die Gr ...... rpern eine Sonderstellung ein.
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Правильный тетраэдр имеет 12 в ...... енной подгруппой A4 группы S4.
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Kvaredra simetrio
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Tetraedergruppe
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Tetrahedral symmetry
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Тетраэдральная симметрия
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