Filling Boxes
A pentacube is a polycube of five cubes. Twelve of the 29 pentacubes correspond to the twelve pentominoes extruded to a depth of one square. A pentacube puzzle or 3D pentomino puzzle, amounts to filling a 3-dimensional box with these 1-layer pentacubes, i.e. cover it without overlap and without gaps. Each of the 12 pentacubes consists of 5 unit cubes, and are like 2D pentominoes but with unit thickness. Clearly the box must have a volume of 60 units. Possible sizes are 2×3×10, 2×5×6 and 3×4×5. Following are several solutions.
Alternatively one could also consider combinations of five cubes that are themselves 3D, i.e., are not part of one layer of cubes. However, in addition to the 12 extruded pentominoes, 6 sets of chiral pairs and 5 pieces make total 29 pieces, resulting 145 cubes, which will not make a 3D box.
Read more about this topic: Pentomino
Famous quotes containing the words filling and/or boxes:
“Religious faith is a most filling vapor.
It swirls occluded in us under tight
Compression to uplift us out of weight....”
—Robert Frost (1874–1963)
“To save the theatre, the theatre must be destroyed, the actors and actresses must all die of the plague. They poison the air, they make art impossible. It is not drama that they play, but pieces for the theatre. We should return to the Greeks, play in the open air: the drama dies of stalls and boxes and evening dress, and people who come to digest their dinner.”
—Eleonora Duse (1858–1924)