Hyperbolic and Higher Dynkin Diagrams
The set of compact and noncompact hyperbolic Dynkin graphs has been enumerated. All rank 3 hyperbolic graphs are compact. Compact hyperbolic Dynkin diagrams exist up to rank 5, and noncompact hyperbolic graphs exist up to rank 10.
The 238 enumerated hyperbolic groups (compact and noncompact) are named as: Hi(n), for rank n, and counting i=1,2,3... for each rank.
| Rank | Total | Compact |
|---|---|---|
| 3 | 123 | 31 |
| 4 | 53 | 3 |
| 5 | 22 | 1 |
| 6 | 22 | 0 |
| 7 | 4 | 0 |
| 8 | 5 | 0 |
| 9 | 5 | 0 |
| 10 | 4 | 0 |
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