Back in 2000, I had an insight into vaulted arches. I had been developing triangular interlocking block as a masonry system, and had devised of a method for making cylinders from these triangular blocks.
A cylindrical section can be turned horizontally to create a vaulted arch, like a roman or circular or barrel vault.
People are largely used to living in a square-cornered building or house. There is something fundamental to the human psyche that looks to straight walls and square corners within a living space as a standard which sets people at ease. Domes and round buildings make up a tiny fraction of habitable structures: almost all buildings have straight walls and square corners. As you read this now, look around you at the building you are in. I'd be willing to bet that it has straight walls and square corners. If not, you are in a very tiny minority, living in an "alternative" structure.
It is a challenge to make a vaulted arch roof system sit atop a square cornered building. In my own masonry approach, which uses triangular block to assemble a cylinder or arch, the triangles can be assembled to provide a helical or spiral edge. A helix or spiral has translation and rotation, and the 'helicity' or angle of 'spiralness' can be varied. Think of stretching a slinky: the spiral angle of translation and rotation can be varied, from shallow to steep angles of helicity.
If the translation versus rotation of a given cylindrical section is equal to the radius of the cylinder versus 90 degrees, then this helicicty can be placed atop a right-angled base. It is thus possible to place vaulted arches atop a right-angled structure. The right angle can be a "turn-in" as shown below, where the angle between walls is simply 90 degrees, as shown below. (taken from one of my patents)
Below is shown a structure where the vaulted arches are shown as a "turn out" where the walls meet at 270 degrees. In the case of both a "turn-in" and a "turn-out" a gap is created between the helical edges of the abutting arches where they meet at a corner. This gap is satisfied by a larger spherical section. Specifically, if the arches are taken as having a raius of 1.0, then the larger spherical section that fills the gap has a radius of 1.5 (If you'd like to see these images better, just click on them to see a larger view).
This sort of arrangement provides extensive design flexibility. One, two, three or four vaulted arches can meet at right angles to each other, merging seamlessly into a larger dome or spherical section.
This arrangement creates some very interesting possibilities far outside the realm of masonry. Could this arrangement have something to do with the structure of DNA and the "magic" of reproduction? We'll take a look at this next time, including a discussion of centromeres and telomeres.