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