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  "body": "\n## Summary\n\nThe Monge point of a [[tetrahedron|JFX8ASQS3E]] is the common point of six planes.\nEach of them passes through the midpoint of an edge and is perpendicular to the opposite edge.\nIt is the reflection of the circumcentre in the [[centroid|0X7EEWES5G]].\nIt plays the role in a tetrahedron that the [[orthocentre|0WB619CA0V]] plays in a triangle, because the altitudes of a tetrahedron need not meet.\nThe definition extends to every [[simplex|YX1DJK2QAG]] of dimension at least $2$, and for a triangle it gives the orthocentre.\n\n## Explanations\n\n### L1 human\n\nIn a triangle, the three altitudes always meet at one point, the orthocentre.\nIn a tetrahedron, the four altitudes usually miss each other.\nGaspard Monge found a replacement: for each edge, take the plane through its midpoint at right angles to the opposite edge.\nThe six planes always meet at one point, the Monge point.\nIt lies on the line through the circumcentre and the centroid, on the other side of the centroid at the same distance.\n",
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