Given a finite set K0 of points (in the plane or space). The sequence of sets K1,K2,...,Kn,... is constructed according to the rule: we take all the points of Ki, add all the symmetric points with respect to all its points, and, thus obtain Ki+1. a) Let K0 consist of two points A and B with the distance 1 unit between them. For what n the set Kn contains the point that is 1000 units far from A? b) Let K0 consist of three points that are the vertices of the equilateral triangle with the unit square. Find the area of minimal convex polygon containing Kn.K0 below is the set of the unit volume tetrahedron vertices. c) How many faces contain the minimal convex polyhedron containing K1? d) What is the volume of the above mentioned polyhedron? e) What is the volume of the minimal convex polyhedron containing Kn? combinatorial geometryconvex polygonconvex polyhedronconvexpoints in space