It is interesting to play with space-filling shapes in architectural design, just to see what can be created and examine their significance to architecture and design. Tessellating polyhedra is a big subject. Part of it are the forms which are created when stacking spheres are converted in to space filling polyhedra. These are useful because they represent some of the most compact arrangements of forms. Regularly stacked spheres occupy approximately 74% of space.
In architecture and design, it points to geometric shapes that offer a low surface area to volume ratio, with a potentially low energy loss through the envelope, or components which might prove easier to move and transport.
There are several ways to stack spheres in compact arrangements, but they seem to fall in to two basic arrangements. Stacking spheres with a square base also creates an arrangement with a triangular base on the diagonal. Working with a triangular base, the stacking arrangement offers the opportunity to rotate the second layer through 60º. The spheres still stack but create different arrangements and different space filling polyhedra.
Matching the arrangement of the layers gives a trapezo-rhombic dodecahedron as a space-filling polyhedra.
|Trapezo-rhombic dodecahedron to rhombic dodecahedron|
slicing through the horizontal plane, making a mirror image and reapplying
It also replicates the arrangement of atoms and crystal structures in nature.
|Polyhedra and Architecture|