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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![](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png) ![](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png) ![](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png)
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![](//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png) ![](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png)
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![](//upload.wikimedia.org/wikipedia/commons/b/bc/CDel_label2.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/2/21/CDel_2a2b.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png)
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![](//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png) ![](//upload.wikimedia.org/wikipedia/commons/8/87/CDel_3ab-cross.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/9/90/CDel_label4.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/b/b3/CDel_labelp.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/c/cc/CDel_labelinfin.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/1/16/CDel_2.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png)
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![](//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png) ![](//upload.wikimedia.org/wikipedia/commons/5/5a/CDel_2a2b-cross.png)
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![](//upload.wikimedia.org/wikipedia/commons/b/bc/CDel_label2.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/f/f0/CDel_2xa2xb-cross.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![](//upload.wikimedia.org/wikipedia/commons/a/a1/CDel_split1.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/d/d5/CDel_3ab.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![](//upload.wikimedia.org/wikipedia/commons/a/a1/CDel_split1.png) ![](//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png) ![](//upload.wikimedia.org/wikipedia/commons/d/d5/CDel_3ab.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/5/5e/CDel_node.png) ![](//upload.wikimedia.org/wikipedia/commons/a/a1/CDel_split1.png) ![](//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png) ![](//upload.wikimedia.org/wikipedia/commons/d/d5/CDel_3ab.png) ![](//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_nodes.png) ![](//upload.wikimedia.org/wikipedia/commons/3/32/CDel_split2.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/4/46/CDel_3a3b-cross.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/5/5a/CDel_2a2b-cross.png)
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![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/f/f0/CDel_2xa2xb-cross.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/9/90/CDel_label4.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/2/2f/CDel_4a4b-cross.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/2/2f/CDel_4a4b-cross.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/7/7a/CDel_4a4b.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/9/90/CDel_label4.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/7/7a/CDel_4a4b.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/2/2c/CDel_splitcross.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/1/1f/CDel_label5.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/d/d2/CDel_5a5b.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png)
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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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![](//upload.wikimedia.org/wikipedia/commons/c/cc/CDel_labelinfin.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png) ![](//upload.wikimedia.org/wikipedia/commons/f/fb/CDel_iaib.png) ![](//upload.wikimedia.org/wikipedia/commons/4/43/CDel_branch.png)
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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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