Vanishing Space Puzzle

This puzzle is from the classic book "Puzzles Old and New" by Jerry Slocum and Jack Botermans. There are 5 pieces made from 14 spheres. One can pack the box with all 5 pieces, or with only 4 pieces. In the second case the box still appears completely full, with no room for the additional sphere. Where did that extra space go?

Two versions of this puzzle are included here. The original version uses spheres and the second uses rhombicuboctahedra (RCO). The same box can be used for either set of pieces. The sphere or RCO diameter is 2 cm. The puzzle seems quite different using spheres compared with RCO. Try both and see what you think.

To make the RCO version, simply print one copy of each of the "RCO" pieces. No supports are needed. The base of several of the pieces are quite small, so you will need a perfectly adhered first layer. Also print a copy of the box and lid.

To make the sphere version, print two copies of each "Sphere" half-piece. No supports are needed.