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  "body": "\n## Summary\n\nAn $n$-simplex is the [[convex hull|0FQSDC2EQ2]] of $n + 1$ points in general position, the simplest convex shape of dimension $n$.\nA point, a segment, a [[triangle|0CTNFGYMM2]] and a [[tetrahedron|JFX8ASQS3E]] are the simplices of dimensions $0$ to $3$.\nSimplices are the building blocks of [[simplicial complexes|V8GZ0W1ZZ5]] in topology and the cells of triangulations in geometry.\nMany notions of triangle geometry, such as the circumsphere and the centroid, extend to simplices.\n\n## Explanations\n\n### L1 human\n\nStart with a point.\nAdd a second point and fill in between: a segment.\nAdd a third point off the line and fill in: a triangle.\nAdd a fourth point off the plane and fill in: a tetrahedron.\nEach step adds one point in a new direction, and the $n$-simplex is what you get after $n$ steps.\n",
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