User:Tomruen/Coxeter foldings
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Let me try using Coxeter–Dynkin_diagram#Geometric_foldings to express Coxeter planes as Coxeter numbers and all degrees of fundamental invariants. Foldings are shown by marking node with colors, re and blue, which map to node 1 or 2 in the rank 2 folded group.
More information Coxetergroup, Coxeterdiagram ...
Coxeter group |
Coxeter diagram |
Degrees | Coxeter planes |
---|---|---|---|
A2 | 2, 3 | A1, A2 | |
B2 | 2, 4 | A1, B2 | |
H2 | 2, 5 | A1, H2 | |
A3 | 2, 3, 4 | A1, A2, A3 | |
B3 | 2, 4, 6 | A1, B2, A2=B3 | |
H3 | 2, 6, 10 | A1, A2, H2=H3 | |
A4 | 2, 3, 4, 5 | A1, A2, A3, A4 | |
B4 | 2, 4, 6, 8 | A1, A3, B2, A2=B3, B4 | |
D4 | 2, 4, 6 | A1, A3, A2=D4 | |
F4 | 2, 6, 8, 12 | A1, A3=B2, A2=B3, F4 | |
H4 | 2, 12, 20, 30 | A1, A2, A3, H2=H3, H4 | |
A5 | 2, 3, 4, 5, 6 | A1, A2, A3, A4, A5 | |
B5 | 2, 4, 6, 8, 10 | A1, A3=B2, A2=B3, B4, A4=B5 | |
D5 | 2, 4, 6, 8; 5 | A1, A3, A2=D4, D5; A4 | |
A6 | 2, 3, 4, 5, 6, 7 | A1, A2, A3, A4, A5, A6 | |
B6 | 2, 4, 6, 8, 10, 12 | A1, A3=B2, A2=B3, B4, A4=B5, B6 | |
D6 | 2, 4, 6, 8, 10 | ||
E6 | 2, 5, 6, 8, 9, 12 | A1, A4, A2=D4=A5, A3=D5, ?, E6 | |
E7 | 2, 6, 8, 10, 12, 14, 18 | ||
E8 | 2, 8, 12, 14, 18, 20, 24, 30 |
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