## Drilled Pentacubes

The P-pentomino and a small pyramid with five cubes seem to be the most promising pieces to drill, because boxes can easily be filled with them.
Torsten Silke has a complete list for all boxes,
which can be constructed with these pieces, if there are no holes.

I took the 10 P-pentominoes with one hole to make a 5x5x2 box and the 45 P-pentominoes with two holes to make a 3x3x25 box.
What about other boxes?

The set of P-pentominoes with 3 holes has 120 elements with a total volume of 600. This seems to be interesting for constructions,
but I haven't got a solution so far.

Drilling the small pyramid gives the same numbers of pieces as with the P-pentomino. A solution for the 5x5x2 is possible, too, but 45 pyramids
don't fit into a 3x3x25 box even if the holes needn't match.

Index

Home