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Construct a solid with 14 faces by cutting off all 8 corners

Source: IMO LongList 1988, South Korea 5, Problem 66 of ILL

November 3, 2005

geometry3D geometrygeometry unsolved

Problem Statement

Let

C

be a cube with edges of length 2. Construct a solid with fourteen faces by cutting off all eight corners at

C,

keeping the new faces perpendicular to the diagonals of the cube, and keeping the newly formed faces indentical. If at the conclusion of this process the fourteen faces so have the same area, find the area of each of face of the new solid.

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