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

Source: Tuymaada 1998 p4

April 28, 2019
geometrytetrahedronplanesDissecting plane3D geometrysolid geometry

Problem Statement

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.
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