at least two points of , the subset is an ovoid (or an oval, if ) within the hyperplane .

For finite projective spaces of dimension (i.e., the point set is finite, the space is pappian), the following result is true:
* If is an ovoid in a finite projective space of dimension , then .
:(In the finite case, ovoids exist only in 3-dimensional spaces.)
*In a finite projective space of order (i.e. any line contains exactly points) and dimension any pointset is an ovoid if and only if and no three points are collinear