In this blog I have written much about the “design
flexibility” inherent to a triangular block masonry design system. What do I really mean by this “design
flexibility”?

Let’s start with the basics: a sphere can be made. This is done by approximating the pattern
generated by a regular polyhedron, and filling the polygons (which comprise the
polyhedron) with triangles. For example,
five triangles can form a pentagon, 6 triangles can form a hexagon; hexagons
and pentagons can combine to form a truncated icosahedron (like a soccer ball).

Half of a sphere can be used to construct a dome, or
hemisphere.

The spacing between blocks can be manipulated to “stretch”
the contour or topography of a hemisphere into a catenary shape, like a
catenary dome (thicker and/or thinner mortar joints can achieve this).

Furthermore, triangular blocks can be used to build a
cylinder, as discussed here. A cylinder –known
to mathematicians as a right circular cylinder- can be bisected parallel to its
axis of rotation, to form a rounded or Roman arch.

Sections of round cylinders can also be used to build arches with more than one center. This adds extensive additional design flexibility, and gives the architect/designer many more options to choose from when building with triangular masonry.

Further still, the proportions of the triangular block can
be chosen such that the helicity of the spiral edge allows round arches to
intersect at right angles. This is important
because many people “don’t want to live in a dome.” Domes are often associated with hippies
chasing utopian dreams, faulty buildings left leaky, stinky and smelling of
armpits and patchouli. Many “simply
could not live in a round dome, it’s so 1960’s and I’m stuck on this commune
and it’s unsanitary and my God I have to take a shower now.” The perceived failure of a counter-cultural
revolution takes its toll on architectural design (sorry modern-day hippies, I
don’t mean to offend you; I am talking about public perception).

My point is that most people in western society prefer to be
in a square-cornered building with right angles and rectilinear orthogonal
design. It’s not called the wrong angle;
it’s called the right angle. We can accommodate
the need for right angles in a building, and do so gracefully and beautifully,
around a central hemisphere or dome.

What other things can we provide in terms of “design
flexibility”? How can domes be used to
make buildings that are not necessarily round?
The key to this is to use many smaller domes to fill a larger floor
plan. If we consider domes (or spheres,
for that matter) and how they can be placed close together, then there are
essentially two types of closest packing which are useful for the architect and
designer. There is cubic packing and
there is hexagonal packing. Cubic
packing is less efficient than hexagonal packing, as it uses up more free
space, or creates a larger interstitial gap between adjacent domes.

The interstitial gap between domes is a curved 3 or 4-sided
shape (hexagonal packing creates 3-sided shapes; cubic packing creates 4-sided
shapes). These shapes can be made into a
“pedentive” which provides continuity between adjacent domes in a structure. A pedentive is traditionally how a round
domed roof is placed (for example) on a square or hexagonal building; it fills
the gap between a round dome and the corners of the building.

If several smaller domes are used to make a roofing system
for a large building, they may be arranged as cubic-packed or hexagonally-packed
roofing units. The pedentives between
adjacent domes can be placed atop columns or posts, creating a beautiful open
space with elegant symmetry and arches describing a high strength, symmetrical
and robust roofing arrangement made entirely of triangular block.

This is a photograph of cubic-packed domes with arches and
pedentives as designed and built by Guastavino, using his catalan arch method
which he employed in the 19

^{th}century. This particular example is at the State Education Building in Albany, New York. One can see how elegantly smaller domes can be used to assemble into beautiful large buildings.
Summing up, we can make spheres, domes, catenary domes,
cylinders, arches, many-centered arches, arches at right angles, and finally use a multiplicity of
smaller domes, arches and columns to create a much larger floor plan. All of these features taken together represent
a very broad spectrum of “design flexibility” provided by triangular masonry block.

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