MathDB

4

Part of 1998 Tuymaada Olympiad

Problems(1)

6 planes divide surface and volume of a tetrahedron with equal opposite sides

Source: Tuymaada 1998 p4

4/28/2019
Given the tetrahedron ABCDABCD, whose opposite edges are equal, that is, AB=CD,AC=BDAB=CD, AC=BD and BC=ADBC=AD. Prove that exist exactly 66 planes intersecting the triangular angles of the tetrahedron and dividing the total surface and volume of this tetrahedron in half.
geometrytetrahedronplanesDissecting plane3D geometrysolid geometry