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  "body": "\n## Summary\n\nA convex body is a [[compact|0R6EWFKRCF]] [[convex set|02AS45T3H9]] in $\\R^n$ with nonempty [[interior|0RZH6W98HK]].\nConvex bodies are the main objects of convex geometry: balls, cubes, simplices and all convex polytopes of full dimension are examples.\nVolume, surface area, mixed volumes and the Brunn–Minkowski theory are all developed for convex bodies.\n\n## Explanations\n\n### L1 human\n\nA convex body is a solid, bounded, convex shape that includes its boundary.\nIt must have some thickness in every direction, so a flat disc lying in space does not count as a convex body in $\\R^3$.\nA solid ball, a solid cube and a solid tetrahedron are convex bodies in space.\nA filled triangle is a convex body in the plane.\n",
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