Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Weyl_group
|
| gptkbp:actsOn |
gptkb:n-dimensional_Euclidean_space
|
| gptkbp:alsoKnownAs |
hyperoctahedral group
|
| gptkbp:contains |
Coxeter group D_n as a subgroup
|
| gptkbp:CoxeterMatrix |
m_{ij} = 4 for i=0, j=1; m_{ij} = 3 for |i-j|=1, i,j>0; m_{ij}=2 otherwise
|
| gptkbp:Dynkin_diagram |
n nodes with one double edge
|
| gptkbp:finiteGroup |
yes
|
| gptkbp:generation |
n involutive generators
|
| gptkbp:hasSpecialCase |
B_2 is the symmetry group of the square
B_3 is the symmetry group of the cube and octahedron |
| https://www.w3.org/2000/01/rdf-schema#label |
Coxeter group B n
|
| gptkbp:namedAfter |
gptkb:H.S.M._Coxeter
|
| gptkbp:order |
2^n n!
|
| gptkbp:presentedBy |
<s_0, s_1, ..., s_{n-1} | s_i^2 = 1, (s_i s_j)^{m_{ij}} = 1>
|
| gptkbp:reflectionGroup |
yes
|
| gptkbp:relatedTo |
Coxeter group A_n
Coxeter group D_n |
| gptkbp:relations |
(s_i s_j)^{m_{ij}} = 1
|
| gptkbp:symmetry |
gptkb:n-dimensional_hypercube
n-dimensional cross-polytope |
| gptkbp:type |
finite reflection group
B_n root system |
| gptkbp:WeylGroupOf |
gptkb:Lie_algebra_sp(2n)
Lie algebra so(2n+1) |
| gptkbp:bfsParent |
gptkb:Hypercube
gptkb:Hyperoctahedron |
| gptkbp:bfsLayer |
7
|