Gothic Arches: pointing to the future?

So...  I've developed triangular blocks to build cylinders.  They can also be used to make arches.  How can arches be made to sit on square-cornered structures, if those arches are made from triangular block?

Describing geometry with words is very difficult, as anyone who's bothered to read this blog can probably attest!  Sorry folks, but it's a challenge!  Today I'll look at lots of images to try and give the reader some familiarity with this subject.  They're also very cool to look at.  This is the sort of thing I want to be able to do with manufactured block.

Here's one example of arches at right angles to each other.  Note the diagonal ribs.

Here's another example of arches at right angles to each other.  Note how they rest on pillars.  I can do this too with my masonry system.  This would make for a pretty cool house!

Here are sketches of a ribbed vault and a gothic vault.  My system is something of a hybrid between these two.

Here is another example of arches at 90 degrees to each other.  Again, note the diagonal ribs.

Yet another example of arches at right angles to each other.  This is romanesque.

Here's a schematic showing two arches (barrel vaults) intersecting at right angles to each other.

Here's a free body diagram showing stress analysis of individual masonry units in an arch, known as "voussoirs."  It is better to have short "block-like" segments instead of long skinny ones.

Having shown some images of arches meeting at right angles, tomorrow we'll see how this problem is essentially the ancient problem of "squaring a circle" and we'll look at what exactly that means.  Below is an ancient image of this problem.  I love how it's drawn on a brick wall, which is the specific realm we're looking at.