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  "body": "\n## Summary\n\nAn ovoid is a set of points of a [[projective space|ZT9A6JK8QF]] that looks like a sphere from the point of view of incidence.\nEvery line meets it in at most two points, and at each of its points the tangent lines fill a hyperplane.\nOvoids in three-dimensional space are the spatial analogue of [[ovals|7B03TB64N9]] in a plane.\nThey give Möbius planes and generalized quadrangles, and finite ovoids are a main topic of Galois geometry.\n\n## Explanations\n\n### L1 human\n\nThink of a sphere in space, completed with points at infinity.\nA line pierces a sphere in at most two points, and the lines that just touch the sphere at a point make up its tangent plane.\nAn ovoid is any set of points with these two properties, defined only through points, lines and planes.\nOver a finite field with $q$ elements, an ovoid of three-dimensional projective space has exactly $q^2 + 1$ points.\n",
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