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Similar tetrahedrons

Source: 64 Polish MO 2013 Second Round - Problem 6

April 21, 2018
3D geometrytetrahedronsimilarityPolandgeometry

Problem Statement

Decide, whether exist tetrahedrons TT, T′T' with walls S1S_1, S2S_2, S3S_3, S4S_4 and S1′S_1', S2′S_2', S3′S_3', S4′S_4', respectively, such that for i=1,2,3,4i = 1, 2, 3, 4 triangle SiS_i is similar to triangle Si′S_i', but despite this, tetrahedron TT is not similar to tetrahedron T′T'.
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