These “Bubble Coasters” were formed using the “Weaire–Phelan structure,” the most mathematically efficient way for equal-sized bubbles to fit together to make foam.
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.
The coasters are sliced from a matrix of Weaire–Phelan structure rotated around a diagonal axis in 10-degree increments. The pattern is most visible in the slices at or near 0 or 90 degrees, and less so in the others. Print them all or choose the style you like best. The pictures above show coaster 10, 20, 30 and 40.
Note that some of the coasters have bubble holes that protrude all the way through.
I suggest not using supports. The small amount of print fail that you get will either not be visible or will be easily removed. Any support structures that extend up into the bubble spaces will be very hard to remove.
To get a better understanding of the Weaire–Phelan structure, check out these “Bubble Blocks”: https://www.thingiverse.com/thing:4765089. There is a good introduction to the “Weaire–Phelan structure” here: http://www.steelpillow.com/polyhedra/wp/wp.html
See here for a similarly designed “Bubble Bowl”: https://www.thingiverse.com/thing:4765118
And here for some other mathematically inspired coasters: https://www.thingiverse.com/thing:4732598
