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  "body": "\n## Summary\n\nA cyclic polytope is the [[convex hull|0FQSDC2EQ2]] of $n \\ge d + 1$ distinct points on the moment curve $t \\mapsto (t, t^2, \\dots, t^d)$ in $\\R^d$.\nIts combinatorial type depends only on the number $n$ of points and the dimension $d$, and it is denoted $C(n, d)$.\nCyclic polytopes are [[simplicial|YVJ15PGKDM]] and [[neighborly|9V4PR1RVXW]].\nThey have the largest number of faces of each dimension among all $d$-polytopes with $n$ vertices, which is the content of the [[upper bound theorem|BH8R1M1KVF]].\n\n## Explanations\n\n### L1 human\n\nPick points on a curve that bends in every direction of space, such as $(t, t^2, t^3)$, and take the solid they span.\nThe curve bends so much that many sets of points become faces.\nIn four dimensions, any two of the points are joined by an edge of the solid.\nThat is far more edges than a three-dimensional solid could have with the same number of corners.\n",
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