Hyperbolic Volume

The hyperbolic volume of the knot complement of a hyperbolic knot is a knot invariant. Adams (1994) lists the hyperbolic volumes for knots and links.

The hyperbolic volume of the figure eight knot is known exactly. No closed forms are known for most (if not all) others.

REFERENCES:

Adams, C. C. "Table of Knots, Links, and Knot and Link Invariants." Appendix in The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp. 279-290, 1994.

Adams, C.; Hildebrand, M.; and Weeks, J. "Hyperbolic Invariants of Knots and Links." Trans. Amer. Math. Soc. 326, 1-56, 1991.