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- Hyperoctahedral_group abstract "In mathematics, a hyperoctahedral group is an important type of group that can be realized as the group of symmetries of a hypercube or of a cross-polytope. It was named by Alfred Young in 1930. Groups of this type are identified by a parameter n, the dimension of the hypercube.As a Coxeter group it is of type Bn = Cn, and as a Weyl group it is associated to the orthogonal groups in odd dimensions. As a wreath product it is where is the symmetric group of degree n. As a permutation group, the group is the signed symmetric group of permutations π either of the set { −n, −n + 1, ..., −1, 1, 2, ..., n } or of the set { −n, −n + 1, ..., n } such that π(i) = −π(−i) for all i. As a matrix group, it can be described as the group of n×n orthogonal matrices whose entries are all integers. The representation theory of the hyperoctahedral group was described by (Young 1930) according to (Kerber 1971, p. 2).In three dimensions, the hyperoctahedral group is known as O×S2 where O≅S4 is the octahedral group, and S2 is a symmetric group (equivalently, cyclic group) of order 2. Geometric figures in three dimensions with this symmetry group are said to have octahedral symmetry. In two dimensions, the hyperoctahedral group is known as the dihedral group of order eight, describing the symmetry of a square.".
- Hyperoctahedral_group thumbnail C2_group_circle_domains.png?width=300.
- Hyperoctahedral_group wikiPageID "24268961".
- Hyperoctahedral_group wikiPageRevisionID "581730503".
- Hyperoctahedral_group hasPhotoCollection Hyperoctahedral_group.
- Hyperoctahedral_group subject Category:Finite_reflection_groups.
- Hyperoctahedral_group type Abstraction100002137.
- Hyperoctahedral_group type FiniteReflectionGroups.
- Hyperoctahedral_group type Group100031264.
- Hyperoctahedral_group comment "In mathematics, a hyperoctahedral group is an important type of group that can be realized as the group of symmetries of a hypercube or of a cross-polytope. It was named by Alfred Young in 1930. Groups of this type are identified by a parameter n, the dimension of the hypercube.As a Coxeter group it is of type Bn = Cn, and as a Weyl group it is associated to the orthogonal groups in odd dimensions. As a wreath product it is where is the symmetric group of degree n.".
- Hyperoctahedral_group label "Hyperoctahedral group".
- Hyperoctahedral_group sameAs m.07s78zb.
- Hyperoctahedral_group sameAs Q5958362.
- Hyperoctahedral_group sameAs Q5958362.
- Hyperoctahedral_group sameAs Hyperoctahedral_group.
- Hyperoctahedral_group wasDerivedFrom Hyperoctahedral_group?oldid=581730503.
- Hyperoctahedral_group depiction C2_group_circle_domains.png.
- Hyperoctahedral_group isPrimaryTopicOf Hyperoctahedral_group.
