Hyperbolic knot census

The simplest knots arranged according to the complexity of their complements, rather than by crossing number as is usually done. See the very interesting paper by Callahan, Dean, and Weeks describing the census (referenced below).

Click on an image to bring up a 3D interactive viewer (requires Java).


k21

k31

k32

k41

k42

k43

k44

k51

k52

k53

k54

k55

k56

k57

k58

k59

k510

k511

k512

k513

k514

k515

k516

k517

k518

k519

k520

k521

k522

k61

k62

k63

k64

k65

k66

k67

k68

k69

k610

k611

k612

k613

k614

k615

k616

k617

k618

k619

k620

k621

k622

k623

k624

k625

k626

k627

k628

k629

k630

k631

k632

k633

k634

k635

k636

k637

k638

k639

k640

k641

k642

k643

Original knot descriptions (before relaxation) courtesy of John Dean. The paper is Callahan, P. J., Dean, J. C. and Weeks, J. R. , The simplest hyperbolic knots, J. Knot Theory Ramifications, 8 (3), (1999), p. 279--297

Postscript version 3: k6.8.ps, k6.9.ps

PostScript and PDF versions of k610 as a closed braid and after simplification (go to Figure 8.14).

Go to the KnotPlot Site or Rob Scharein's home page.