tetrahedral group

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• Binary tetrahedral group — In mathematics, the binary tetrahedral group is an extension of the tetrahedral group T of order 12 by a cyclic group of order 2.It is the binary polyhedral group corresponding to the tetrahedral group, and as such can be defined as the preimage… …   Wikipedia

• Tetrahedral symmetry — A regular tetrahedron has 12 rotational (or orientation preserving) symmetries, and a total of 24 symmetries including transformations that combine a reflection and a rotation.The group of symmetries that includes reflections is isomorphic to S 4 …   Wikipedia

• Group action — This article is about the mathematical concept. For the sociology term, see group action (sociology). Given an equilateral triangle, the counterclockwise rotation by 120° around the center of the triangle acts on the set of vertices of the… …   Wikipedia

• Tetrahedral molecular geometry — In a Tetrahedral molecular geometry a central atom is located at the center with four substituents that are located at the corners of a tetrahedron. The bond angles are cos−1(−1/3) ≈ 109.5° when all four substituents are the same, as in CH4. This …   Wikipedia

• Group (mathematics) — This article covers basic notions. For advanced topics, see Group theory. The possible manipulations of this Rubik s Cube form a group. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines …   Wikipedia

• Tetrahedral carbonyl addition compound — A tetrahedral carbonyl addition compound is an organic compound formed by nucleophilic addition to a carbonyl compound such as an aldehyde or ketone. This provides the carbon with four temporary bonds, one of which is broken when the leaving… …   Wikipedia

• Binary icosahedral group — In mathematics, the binary icosahedral group is an extension of the icosahedral group I of order 60 by a cyclic group of order 2. It can be defined as the preimage of the icosahedral group under the 2:1 covering homomorphism:mathrm{Sp}(1) o… …   Wikipedia

• Binary octahedral group — In mathematics, the binary octahedral group is an extension of the octahedral group O of order 24 by a cyclic group of order 2. It can be defined as the preimage of the octahedral group under the 2:1 covering homomorphism:mathrm{Sp}(1) o… …   Wikipedia

• Symmetry group — Not to be confused with Symmetric group. This article is about the abstract algebraic structures. For other meanings, see Symmetry group (disambiguation). A tetrahedron can be placed in 12 distinct positions by rotation alone. These are… …   Wikipedia

• Dicyclic group — In group theory, a dicyclic group (notation Dicn) is a member of a class of non abelian groups of order 4n (n > 1). It is an extension of the cyclic group of order 2 by a cyclic group of order 2n, giving the name di cyclic. In the… …   Wikipedia

• Quaternion group — In group theory, the quaternion group is a non abelian group of order 8. It is often denoted by Q and written in multiplicative form, with the following 8 elements : Q = {1, −1, i , − i , j , − j , k , − k }Here 1 is the identity element, (−1)2 …   Wikipedia