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  "body": "\n## Example\n\nThe *figure-eight knot* is the [[knot|QYEAZTYGPT]] obtained by closing up the figure-eight knot of rope.\nIts standard diagram has $4$ crossings that alternate over and under along the curve.\nOne parametrization of it is\n$$t \\mapsto \\bigl((2 + \\cos 2t) \\cos 3t, \\ (2 + \\cos 2t) \\sin 3t, \\ \\sin 4t\\bigr), \\qquad t \\in [0, 2\\pi).$$\nIts [[crossing number|SWJZ4QRF9W]] is $4$.\nIndeed, the only knots with crossing number less than $4$ are the unknot and the two trefoils, and the figure-eight knot is neither.\n\n## Remarks\n\nIts Alexander polynomial is $-t^{-1} + 3 - t$, which differs from that of the unknot, $1$, and from that of the trefoil, $t^{-1} - 1 + t$.\nIt is not [[tricolorable|KNAGK0W65G]], because its determinant is $5$, not divisible by $3$.\nIt is equivalent to its mirror image, unlike the trefoil.\nIt is a [[hyperbolic knot|K47G2Q24DT]]: its complement carries a complete hyperbolic metric of finite volume, made of two regular ideal tetrahedra.\n\n## Explanations\n\n### L1 human\n\nThe figure-eight knot is the next simplest knot after the trefoil, with four crossings in its simplest picture.\nIts name comes from the figure-eight knot that climbers and sailors tie, with the ends joined.\nUnlike the trefoil, it can be deformed into its own mirror image.\n",
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