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  "body": "\n## Example\n\nThe *Desargues configuration* is a [[configuration|Q2QFXPP9EE]] $(10_3)$ in the projective plane.\nTake two triangles $a_1 a_2 a_3$ and $b_1 b_2 b_3$ in perspective from a point $O$, so that $O$, $a_i$, $b_i$ are collinear for $i = 1, 2, 3$.\nLet $c_{ij}$ be the intersection of the sides $a_i a_j$ and $b_i b_j$.\nBy [[Desargues's theorem|5Z19Y02MME]], the three points $c_{12}$, $c_{13}$, $c_{23}$ lie on a line, the axis.\n\nIts $10$ points are $O$, the six vertices and the three points $c_{ij}$.\nIts $10$ lines are the three lines $O a_i b_i$, the six sides of the triangles and the axis.\nCheck: each line has $3$ of the points, for instance the side $a_1 a_2$ contains $a_1$, $a_2$, $c_{12}$.\nEach point lies on $3$ lines.\nFor instance, $O$ lies on the lines $O a_i b_i$, the vertex $a_1$ on $O a_1 b_1$, $a_1 a_2$, $a_1 a_3$, and $c_{12}$ on $a_1 a_2$, $b_1 b_2$ and the axis.\n\nA combinatorial model: the points are the $2$-element subsets of $\\set{1, 2, 3, 4, 5}$ and the lines are the $3$-element subsets, with incidence by inclusion.\nEach $3$-set contains three $2$-sets, and each $2$-set lies in three $3$-sets.\nIts incidence graph is the Desargues graph.\n\n## Explanations\n\n### L1 human\n\nDraw two triangles whose corresponding corners are lined up with a common point.\nExtend the corresponding sides until they cross; the three crossing points then lie on one line.\nThe whole drawing has $10$ points and $10$ lines, with $3$ points on each line and $3$ lines through each point.\nThe pattern is perfectly balanced, and any of its $10$ points can play the role of the center.\n",
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