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regular octahedron inscribed into regular dodecahedron

Source: 2009 Sharygin Geometry Olympiad Final Round problem 8 grade 10

July 26, 2018
geometry3D geometrydodecahedronoctahedron

Problem Statement

Can the regular octahedron be inscribed into regular dodecahedron in such way that all vertices of octahedron be the vertices of dodecahedron?
(B.Frenkin)