This vase is formed using the “Weaire–Phelan structure,” the most mathematically efficient way for equal-sized bubbles to fit together to make foam. See here for video: https://youtu.be/f4YIuS_-hSE
This vase demonstrates a transition from a polyhedral representation of the Weaire–Phelan structure at the top to Weaire–Phelan foam at the bottom.
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
