ASU 255 All Soviet Union MO 1978 sequence of points in plane and in space
Source:
July 11, 2019
combinatorial geometryconvex polygonconvex polyhedronconvexpoints in space
Problem Statement
Given a finite set of points (in the plane or space). The sequence of sets is constructed according to the rule: we take all the points of , add all the symmetric points with respect to all its points, and, thus obtain . a) Let consist of two points and with the distance unit between them. For what the set contains the point that is units far from ? b) Let consist of three points that are the vertices of the equilateral triangle with the unit square. Find the area of minimal convex polygon containing below is the set of the unit volume tetrahedron vertices. c) How many faces contain the minimal convex polyhedron containing ? d) What is the volume of the above mentioned polyhedron? e) What is the volume of the minimal convex polyhedron containing ?