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gptkbp:instanceOf
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gptkb:Weyl_group
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gptkbp:actsOn
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gptkb:n-dimensional_Euclidean_space
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gptkbp:alsoKnownAs
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hyperoctahedral group
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gptkbp:contains
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symmetric group Sn
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gptkbp:CoxeterMatrix
|
entries: 4 between first two nodes, 3 elsewhere
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gptkbp:discoveredBy
|
gptkb:H.S.M._Coxeter
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gptkbp:Dynkin_diagram
|
n nodes with one double edge
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gptkbp:generation
|
n
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gptkbp:hasSpecialCase
|
B1 is C2
B2 is dihedral group of order 8
B3 is symmetry group of cube
B4 is symmetry group of tesseract
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|
https://www.w3.org/2000/01/rdf-schema#label
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Coxeter group Bn
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gptkbp:isFinite
|
yes
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gptkbp:isomorphicTo
|
signed permutation group
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gptkbp:notation
|
B_n
W(Bn)
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gptkbp:order
|
2^n n!
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gptkbp:presentedBy
|
generators s0, s1, ..., sn-1 with specific relations
|
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gptkbp:reflectionGroup
|
yes
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gptkbp:relatedTo
|
Coxeter group Cn
Coxeter group Dn
|
|
gptkbp:symmetry
|
gptkb:n-dimensional_hypercube
n-dimensional cross-polytope
|
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gptkbp:type
|
finite reflection group
type Bn
|
|
gptkbp:Weyl_group_of
|
Lie algebra so(2n+1)
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gptkbp:bfsParent
|
gptkb:Cross-polytope
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gptkbp:bfsLayer
|
6
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