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volo f set of midpoints of segments of 2 central symmetric reg. tetrahedra

Source: - All-Russian MO 1998 Regional (R4) 11.7

September 17, 2024
geometry3D geometrytetrahedronVolume

Problem Statement

Given two regular tetrahedrons with edges of length 2\sqrt2, transforming into one another with central symmetry. Let Φ\Phi be the set the midpoints of segments whose ends belong to different tetrahedrons. Find the volume of the figure Φ\Phi.
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