Let a space figure consist of n vertices and l lines connecting these vertices, with n=q2+q+1, l≥q2(q+1)2+1, q≥2, q∈N. Suppose the figure satisfies the following conditions: every four vertices are non-coplaner, every vertex is connected by at least one line, and there is a vertex connected by at least p+2 lines. Prove that there exists a space quadrilateral in the figure, i.e. a quadrilateral with four vertices A,B,C,D and four lines AB,BC,CD,DA in the figure. geometry unsolvedgeometry