This soap dish is formed using the “Weaire–Phelan structure,” the most mathematically efficient way for equal-sized bubbles to fit together to make foam.
If your bar of soap made perfect bubbles, this is what they would look like!
The structure is made up of two pentagonal dodecahedra (12-sided) and six tetrakaidecahedra (14-sided) that form a translation unit with a lattice periodicity which is simple cubic. In crystallography, this structure is also known as the A15 Frank-Kasper phase.
See my main page for some other designs based on the Weaire–Phelan structure.
There is a good introduction to the “Weaire–Phelan structure” here: http://www.steelpillow.com/polyhedra/wp/wp.html
