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  "body": "\n## Example\n\nThe *Möbius–Kantor configuration* is the [[configuration|Q2QFXPP9EE]] $(8_3)$: $8$ points and $8$ lines, with $3$ points on each line and $3$ lines through each point.\nUp to isomorphism there is only one $(8_3)$ configuration.\nA model has the points $0, 1, \\dots, 7$ in $\\Z/8\\Z$ and the lines $\\set{i, i + 1, i + 3}$ for $i \\in \\Z/8\\Z$.\n\nCheck: each point $j$ lies on the three lines with $i = j$, $i = j - 1$ and $i = j - 3$.\nThe differences of elements of $\\set{0, 1, 3}$ are $\\pm 1, \\pm 2, \\pm 3$, each obtained once and all distinct modulo $8$.\nSo two points whose difference is one of these lie on exactly one common line, and two points with difference $4$ lie on none.\n\nAnother model: delete one point from the [[affine plane of order $3$|S2NAGK9YHF]], together with the $4$ lines through it.\nThe remaining $8$ points and $8$ lines have $3$ points on each line, and each point lies on $4 - 1 = 3$ of the remaining lines.\n\nThe configuration cannot be realized by points and lines of the real plane, but it can be realized in the complex projective plane.\nIts incidence graph is the Möbius–Kantor graph.\n\n## Explanations\n\n### L1 human\n\nCan you draw two quadrilaterals so that each vertex of one lies on a side of the other, and the other way round?\nMöbius asked this, and the answer is no with real points and straight lines.\nThe combinatorial pattern still exists: $8$ points and $8$ lines, each line through $3$ points and each point on $3$ lines.\nIt can be drawn with complex coordinates, or in the finite plane over the field with $3$ elements.\n",
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