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  "body": "\n## Summary\n\nA unital of order $n$ is a [[block design|4JCSS2Z1BA]] with $n^3 + 1$ points and blocks of $n + 1$ points.\nAny two points lie in exactly one block.\nThe main examples sit inside a [[projective plane|DANFNN8C4Y]] of order $n^2$, where they meet every line in $1$ or $n + 1$ points.\nThe classical example is the Hermitian curve, defined by a [[Hermitian form|48P4A1CX85]] over a field with $n^2$ elements.\n\n## Explanations\n\n### L1 human\n\nA unital is a finite geometry of points and blocks in which two points always share exactly one block.\nIts numbers are fixed by one parameter $n$: there are $n^3 + 1$ points and each block has $n + 1$ points.\nThe standard picture is a curve inside a finite plane whose lines cut it either in one point or in $n + 1$ points.\nFor $n = 2$ one gets $9$ points with blocks of size $3$, sitting inside the plane of order $4$.\n",
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