Today’s puzzles are about fitting regular polihedra into boxes.
1.07 A rectangular box can be filled completely with cubes of dimensions 1 x 1 x 1. When the unit cubes are removed and larger cubes, each having a volume of 2, are placed in the box with their edges parallel to the edges of the box, it turns out that they can only fill 40% of the box. What is a possible set of dimensions for such a box?
1.08 What are the dimensions of the smallest rectangular box that can contain a regular octahedron with unitary edge length?
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