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The figure-eight knot has played an important role historically (and continues to do so) in the theory of 3-manifolds.Sometime in the mid-to-late 1970s, William Thurston showed that the figure-eight was hyperbolic, by decomposing its complement into two ideal hyperbolic tetrahedra.
80%: Origin: Ancient: Related: Stevedore knot, figure-eight loop, figure-eight follow through, directional figure eight: Releasing: Jamming: Typical use: General-purpose stopper knot. Replaces the common overhand knot in many uses. ABoK #420 #520 #570: Conway Notation: 2 2: A/B notation: 4 1: Instructions
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4 1: 4a1 4 6 8 2 [22] 1234:2143 1231\4324 Cinquefoil knot: 5 1: 5a2 6 8 10 2 4 [5] 12345:12345 Three-twist knot: 5 2: 5a1 4 8 10 2 6 [32] 12345:12543 1231\452354 Stevedore knot: 6 1: 6a3 4 8 12 10 2 6 [42] 123456:216543 1231\45632654 6 2 knot: 6 2: 6a2 4 8 10 12 2 6 [312] 123456:234165 1231\45632456 6 3 knot: 6 3: 6a1 4 8 10 2 12 6 [2112 ...
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