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| Space
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Coxeter diagrams
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Bracket notation
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Extended
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| Finite
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S3
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[(2,2,2,2):2]
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[2[4]:2] = [2[4]]
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[4[2[4]:2]] = [4[2[4]]] = [[4,2,4]]
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[(2,2,2,2):3]
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[2[4]:3]
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[4[2[4]:3]] = [[6,2,6]]
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[(2,2,2,2):4]
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[2[4]:4]
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[4[2[4]:4]] = [[8,2,8]]
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[(2,2,2,2):p]
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[2[4]:p]
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[4[2[4]:p]] = [[2p,2,2p]]
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| Affine
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E2
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[(2,2,2,2):∞]
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[2[4]:∞]
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[4[2[4]:∞]] = [[∞,2,∞]] = [4,4]
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[(3,3,3)]
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[3[3]]
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[3[3[3]]] = [6,3]
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| E3
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[(3,3,3,3):2]
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[3[4]:2] = [3[4]]
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[4[3[4]:2]] = [[4,3,4]]
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| E4
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[(3,3,3,3,3):2]
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[3[5]:2] = [3[5]]
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[5[3[5]:2]] = [5[3[5]]]
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| E5
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[(3,3,3,3,3,3):2]
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[3[6]:2] = [3[6]]
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[6[3[6]:2]] = [6[3[6]]]
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| Compact
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H2
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[(3,3,3,3):∞]
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[3[4]:∞]
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[4[3[4]:∞]] = [[∞,3,∞]] = [6,4]
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[(2,3,2,3):∞]
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[(2,3)[2]:∞]
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[2[(2,3)[2]:∞]] = [6,4]
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[(2,2,2,2,2,2):∞]
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[2[6]:∞]
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[6[2[6]:∞]] = [6,4]
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[(4,4,4,4):∞]
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[4[4]:∞]
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[4[4[4]:∞]] = [[∞,4,∞]] = [8,4]
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[(3,4,3,4):∞]
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[(3,4)[2]:∞]
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[2[(3,4)[2]:∞]] = [8,6]
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| H3
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[(3,4,3,4):2]
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[(3,4)[2]:2] = [(3,4)[2]]
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[2[(3,4)[2]]]
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| Paracompact
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H3
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[(4,4,4,4):2]
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[4[4]:2] = [4[4]]
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[4[4[4]:2]] = [[4,4,4]]
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[(3,3,3,3):3]
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[3[4]:3]
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[4[3[4]:3]] = [[6,3,6]]
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| Lorentzian
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L3
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[(5,5,5,5):2]
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[5[4]:2] = [5[4]]
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[4[5[4]:2]] = [[4,10,4]]
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[(∞,∞,∞,∞):2]
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[∞[4]:2] = [∞[4]]
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[4[∞[4]:2]] = [[4,∞,4]]
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[(a,a,a,a):b]
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[a[4]:b]
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[b[a[4]:b]] = [[2b,a,2b]]
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| L4
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[(3,3,3,3,3):3]
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[3[5]:3]
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[5[3[5]:3]]
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