A number of project s I am interested in also relate to my research are the water cube, munich arena, Serpentine Pavilion 2002 to name a few. The algorithms behind some of these projects are extremely complex but interesting. ....The design of this building is based on the Weaire-Phelan structure. But the story behind the design of this building goes back to 36 BC, when Marcus Terentius Varro described two competing theories for why bees have hexagonal honeycombs. The first said: because bees have six legs! The second said: efficiency! You see, a hexagonal lattice lets you divide the plane into cells of equal area with the least possible perimeter per cell. So if the bees want to save wax, that's the pattern they'll pick.
But it's worth noting that honeycomb cells are actually 3-dimensional - and the end of each cell consists of three rhombi that meet at the same angle as bubbles in soap suds!
Now, soap films minimize surface area subject to whatever constraints they encounter. So, a single bubble that holds a given amount of air will form a sphere. But soap suds with lots of bubbles do more complicated things. Take a bubble bath and pay careful attention! You'll see that three bubble faces meet along each edge, at precisely 120 degree angles. And when four bubbles meet at a vertex, they form a pattern with tetrahedral symmetry, with edges meeting at an angle of arccos(-1/3), or about 109.5 degrees.