Genesis of form

Three basic tiling elements of the two dimensional plane can create three dimensionality. It is only the regular hexagon, the square and the equilateral triangle that can perfectly "tile the plane". These three elements are individually combined with the square to make a set of three single level, repeating geometrical tiling patterns. This patterning , if it is alternatively folded at the boundaries between the squares and the hexagons, in a concertina fashion, will allow the hithertoo, two dimensional pattern to become a three dimensional structure. The gain in height is proportional to the loss of surface area of base.