Tiling

I am getting ready to tile my bathroom, so I thought this would be a good occasion to talk about tiling.


The basic steps in tiling today involve gluing the tile to a substrate (concrete floor, etc.), and then grouting the space between the tiles. The tiles are glued with either thin-set mortar or mastic. After tiles are set, mortar is applied between the tiles. This mortar is then usually sealed, and allowed to cure.

There is a long history of exquisite tiling from ancient sites and across much of the globe, it endures and remains functional and vibrant. Here is beautiful tile work from Delphi, Greece.

Here is an ancient Arabesque tile showing fractal geometry.

Here is an ancient Assyrian tile, with a floral motif.

Here is tile from the Topkapi palace, in Istanbul, Turkey.

The Topkapi tiling as an interior arrangement, masterfully executed.

Today most tiles are made as mass-produced unit shapes, which fit together according to a regular repeating pattern, like squares, or triangles or hexagons, etc.

In the world of mathematics, tiling is defined as a two-dimensional pattern resembling a tiled surface. This gets pretty interesting. Regular triangles can tile, squares can tile, hexagons can tile, octagons can tile; but pentagons can NOT tile. If you try to tile together pentagons on a flat surface, you get a gap. Geometers call this gap a “frustration.” Five-fold symmetry does not appear to lend itself to tiling.

Roger Penrose realized that five-fold symmetry could in fact be used for tiling, if done in a quasi-periodic arrangement involving two shapes. There is no regular repetition of geometry, but instead a random element of arrangement which completes the mathematical task of tiling a flat surface. This creates some beautiful patterns. This makes for fun tiling!

A mason's trick

Masons have several "tricks" up their sleeves that they will use in the course of doing work.

One of these tricks is pretty sneaky and rather clever.  It's about insuring that they get paid for their work.

One of the most common jobs a mason is hired for is to build chimneys.  Anyone who has ever worked in construction -as a contractor- probably has their own tales about not being paid by the homeowner, or the main contractor, if you work as a subcontractor.  Here's a trick masons use to make sure they get paid when they build a chimney.

Toward the top of the chimney, a piece of plate glass is placed in the mortar, between bricks.  The plate glass is located so that it obstructs the air flow in the chimney.  If someone tries to start a fire, the chimney won't draw at all, and the house will fill with smoke.  If the homeowner looks up the chimney, they will see the sky, and will wonder "why doesn't this chimney work?"  Now if they haven't paid the mason, he or she can say:  "Pay me and I'll fix it."  After being paid, the mason then breaks the glass and the chimney works fine.

Just a method to ensure payment.   But if you upset the mason while they're working, you might end up with this:

Glass Block: a new design

The block system described in this blog readily lends itself to being made with glass. Today we’ll take a look at glass block, and how it would be suitable for this masonry system.

Glass block has become a fairly widespread construction material. As with concrete block, glass block are currently limited to square and rectangular blocks. This limits the architectural applications of glass block to straight vertical walls and square corners. Some block designs include curved corners, but currently no glass block can be used for spherical or dome sections, as I’m proposing here. It’s interesting to me how regular glass block today says “1980’s” and is not considered current, or ‘in vogue.’

Glass block is manufactured by first forming two pieces of glass, and then joining them while the glass is still warm enough to be moveable (at around 800 degrees F). The two pieces are pinched together in a two-piece mold and allowed to anneal, or cool slowly to reduce thermal stresses and obtain a thermally stable object. If the hot glass is not properly annealed, it will crack some time after it is removed from heat.

Hollow glass block creates a decent thermal insulator, and saves heating and cooling requirements for a given building.

Interestingly (perhaps counter-intuitively) glass has a high strength: higher than concrete in some cases. The theoretical strength of glass is very high, and is only reduced by small surface flaws which create starting points for cracks to begin and significantly lowers the actual strength of glass.

Glass can be greatly strengthened by using a technique called ‘ion substitution.’ Glass typically is made with a flux agent, which lowers the melting temperature of the glass. Sodium is a common flux, and is typically found in silicate glasses. If a sodium silicate glass is immersed in a heated bath, comprised of (for example) potassium compounds (e.g. KOH), then the potassium will migrate into the glass, and replace sodium. Potassium is larger (ionic radius) than sodium, so it ‘stuffs’ the glass and creates compression in the glass; resulting in a much stronger glass. This method could be used to create very high strength architectural glass block.

The block system I’ve been describing in this blog is made on a two-piece mold, without any undercut. This is what is required to make hollow glass block. The block system I’ve been describing is appropriate and suitable for producing hollow architectural block.

The glass block produced from this masonry system can be used to assemble spheres, domes, arches, straight walls, and various combinations of these architectural elements. These blocks will all interlock, they are disposed to conjugate shearing without breaking, they can use a series of tensile elements (e.g., steel cable, Kevlar, etc.) to provide a much higher strength to the entire structure.

Glass block can also be used together with concrete block. This is important because glass block is more expensive than concrete, so it can be used as a highlight feature, and bring some dramatic lighting elements to an overall structure. Glass block can also be used to build a small dome, which could be incorporated as a cupola, or an architectural feature within a building. Imagine a glass dome at the top of a foyer or entryway into a building or house.

The symmetry and hexagonal elements inherent to this masonry system produces a ‘snowflake’ effect, where the architecture has a close resemblance to the beauty and symmetry found in snowflakes.