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  "body": "\n## Example\n\nStart with a round circle $C_1$ in $\\R^3$, and let $D$ be the flat disk that it bounds.\nTake a second closed curve $C_2$, disjoint from $C_1$, that goes down through $D$ and then comes back up through $D$, with one twist.\nIn the standard diagram, $C_2$ has the shape of a figure eight with one self-crossing, and it clasps $C_1$.\nThe union $C_1 \\cup C_2$ is a [[link|1A5WRCNTM3]] with $2$ components, the *Whitehead link*.\nIts standard diagram has $5$ crossings: one crossing of $C_2$ with itself, and four crossings between $C_1$ and $C_2$.\nThe four crossings between the components come in two pairs of opposite signs, so the [[linking number|SFJ329YB9F]] of $C_1$ and $C_2$ is $0$.\nEach component on its own is an [[unknot|1TQ06R4Q66]].\n\n## Remarks\n\nAlthough its linking number is $0$, the Whitehead link is not the unlink of two components: the two curves cannot be separated.\nOne way to see this uses its complement in $S^3$, which carries a complete hyperbolic metric of finite volume.\nThe complement of a split link contains a sphere that separates the components.\nA hyperbolic complement contains no such sphere.\nThe complement is built from one regular ideal octahedron, and its volume is about $3.6639$.\nIts crossing number is $5$.\nIt was studied by J. H. C. Whitehead in his work on contractible open $3$-manifolds.\nTogether with the Hopf link, it shows that the linking number detects some but not all linking.\n\n## Explanations\n\n### L1 human\n\nThe Whitehead link has two loops of string, each unknotted on its own.\nOne loop passes through the other and then hooks back on itself, so that it goes through once in each direction.\nCounting with signs, the loops wind around each other zero times, yet they still cannot be pulled apart.\n",
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