IMO 1988 LL KOR57

Let C be a cube with edges of length 2. Construct a solid with

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IMO 1988 LL KOR57

Origin: KOR

Problem

Let C be a cube with edges of length 2. Construct a solid with fourteen faces by cutting offall eight corners of C, keeping the new faces perpendicular to the diagonals of the cube and keeping the newly formed faces identical. If at the conclusion of this process the fourteen faces so formed have the same area, find the area of each face of the new solid.