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  "body": "\n## Summary\n\nA simplicial polytope is a [[convex polytope|300K6CB1KH]] all of whose [[facets|DPDXN2FJC4]] are simplices.\nIts boundary is then a [[simplicial complex|V8GZ0W1ZZ5]] homeomorphic to a sphere.\nSimplicial polytopes are the natural setting of the face-counting theory of polytopes, including the [[Dehn–Sommerville equations|4WKHF5BCTA]] and the [[g-theorem|4CZMWQVC30]].\nPoints in general position always have a simplicial convex hull, so \"most\" polytopes are simplicial.\n\n## Explanations\n\n### L1 human\n\nA simplex is the simplest solid of its dimension: a segment, a triangle, a tetrahedron, and so on.\nA polytope is simplicial when every face on its surface is a simplex.\nIn three dimensions this means every face is a triangle.\nThe octahedron and the icosahedron are simplicial; the cube is not, because its faces are squares.\n",
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