A cylinder made of triangular bricks can be assembled with a helical edge. “Helicity” refers to translation vs. rotation: thinking of a slinky, if you stretch out the coil, you decrease the helicity. The helicity of a masonry edge can be manipulated by the shape of the triangle.
If the translation is proportional to the radius of the cylinder, and the rotation is equal to 90 degrees; then this proportioned triangle can be assembled with a helical edge that allows arches to intersect at 90 degrees.
This proportioned triangle (in this case, with independent key) looks like this:
Arches made with these blocks can be turned in, like this:
Arches can also be turned out, like this:
Note the gap between the arches where they intersect. This gap can be filled with a larger spherical section or dome. If the cylinders are considered radius 1, then the larger sphere has a radius of 1.5.
The sphere filling this section does not fill it precisely. This is the ancient problem of “squaring a circle,” a fascinating and amusing story of dedicated mathematicians pursuing a Sisyphean task. It is impossible to square a circle, and this was not proven until 1882.
This way of putting together two barrel vaults made from triangular blocks, so that they intersect at a right angle into a larger dome (also made of triangular block) creates extensive additional design flexibility. There are many ways to configure this system.
I’ll be talking about this in much detail over the next several blogs.