Skip to content / Đến nội dung
ThichHocToan.com

IMO 1959–1966 - Longlisted Problems (individual years unknown) Question 20

IMO Shortlist · IMO 1959–1966 - Longlisted Problems (individual years unknown)

Question 20

(HUN) We are given three equal rectangles with the same center in three mutually perpendicular planes, with the long sides also mutually perpendicular. Consider the polyhedron with vertices at the vertices of these rectangles.

(a) Find the volume of this polyhedron;

(b) can this polyhedron be regular, and under what conditions?