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Distance between points is p, intersection between E and P

Source: AustriaMo1970 problem 3

June 29, 2011
geometry3D geometryoctahedronratiogeometry unsolved

Problem Statement

E1E_1 and E2E_2 are parallel planes and their distance is pp. (a) How long is the seitenkante of the regular octahedron such that a side lies in E1E_1 and another in E2E_2? (b) EE is a plane between E1E_1 and E2E_2, parallel to E1E_1 and E2E_2, so that its distances from E1E_1 and E2E_2 are in ratio 1:21:2 Draw the intersection figure of EE and the octahedron for P=432P=4\sqrt{\frac32} cm and justifies, why the that figure must look in such a way