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Polygonal Masonry

The content below was copied with the generous permission of the author Sean Adcock
This article originally appeared in the Summer 2008 issue of Stonechat, produced by the North Wales Branch of the Dry Stone Walling Association of Great BrittanThis entire issue of Stonechat, and many more, are available at http://www.dswales.org.uk/Stonechat.html  
Thank you to Sean for allowing us to provide this content, and please donate to The North Wales Branch.

Wikipedia (http://en.wikipedia.org/wiki/Polygonal_masonry) defines polygonal masonry as:

“A technique of stone construction of the ancient Mediterranean world. True polygonal masonry may be defined as a technique wherein the visible surfaces of the stones are dressed with straight sides or joints, giving the block the appearance of a polygon.” Simple.

Polygonal walls have fascinated me ever since I found a British Standard for Polygonal Masonry whilst researching “Dry Stone Walling”. That of course refers to mortared work such as the cladding shown on the house (left). Mortared work should always have even beds, which is perhaps what makes such cladding eye-catching, if somehow incongruous – probably from years of indoctrination of laying stones true to the horizontal). Whatever the case it always amazes me as to how well the polygons fit together, and from what I’ve seen of dry stone polygonal walls in the flesh and photos they generally exhibit a similar degree of “tightness”.

Tightness in a wall is essentially how well the stones fit together, leaving a minimum of gaps. This is in part dependent on stone size, a tight wall built of large boulders will have noticeable gaps but generally good stone to stone contact, a tight wall built from smaller stone will have next to no discernable gaps. This tightness is generally achieved without a plethora of small stone filling every nook and cranny (except for the inevitable local practices such as in parts of Scotland where every gap is `pinned` after the main building work is completed).

Whilst polygonal walls are a feature of a number of Mediterranean countries, perhaps the most famous polygonal walls are the Inca walls of Peru, of Machu Picchu, Cuzco and Ollantaytambo.

Western Wall, Inka Roq`e`s Palace, Cuzco © F.Menotti

These walls take `tightness` to extremes, as can be seen from the cover photo of the famous ”12 sided stone of Hatunrumiyoc” in the wall of the Inka Roq`e`s palace in Cuzco. The photo right puts this stone in perspective. Although there are of course `looser` versions, the accuracy of the dressing, it is thought achieved only with hammerstones, is truly amazing.

Francesco Menotti in “The Inkas:Last Stage of Stone Masonry Development in the Andes” (Archaeopress 1998) identifies three styles of jointing: natural, rustic and refined (p.36). The refined version is generally found on what would have been the more important buildings with the fitting so good that according to Menotti “a razor blade cannot be stuck in the joint of two blocks”. `Natural` versions include many smaller

Above City wall, Ancient Mycenae, Greece. © S.Adcock

stones (similar to the right hand side of the Mycenae photograph, left). `Rustic` lies somewhere between these, with stone dressing limited, but with a tighter fit and fewer small stones.

Menotti adds further sub-divisions, with “cellular” somewhere between `rustic` and `refined`, and the refined version having a “sedimentary style”

Sedimentary style © F.Menotti

where the stonework is more reminiscent of standard coursed stonework until sometimes when you look closely…

These styles are supplemented by various forms of finishing, and jointing profile. The stone surface might be left natural (coarse) or roughly flattened or even smoothed. Menotti identifies 6 joint profiles (p.37) natural, rough hewed (ie lightly dressed), cushioned and convex (two similar rounded finishes cushioned leaving more of a `bull-nose`), bevelled, and flat. The Bevelled, cushioned and convex joints produce perhaps the most striking walls which seem somehow unreal and Menotti describes these walls as having a “plastic” appearance (p.36) illustrated by the stones in this `cyclopean` (i.e. built by giants) wall.

Saqsaywaman walls, see llama, right, for scale. © F.Menotti

Cellular construction, Colcampata Palace © F.Menotti

Despite wikipedia`s definition, not all polygonal walls are built from straight sided stone as can be seen in this example from Delphi, Greece (right).

From times of the Spanish conquest `modern` towns and cities in Peru have been levelled by earthquakes whilst the Inca walls have largely stood firm. Apparently earth quake prone Japan also has polygonal walls and then there is also Wikipedia`s “Ancient Mediterranean” world, the Balearics, Italy and Greece at least have polygonal walls, and are earthquake prone. Delphi was destroyed by an earthquake the terrace wall survived laying buried under the rubble of the temple until `modern` excavations unearthed it.

Retaining wall below Temple of Apollo, Delphi, Greece. © S.Adcock

So how do polygonal walls work…

Polygonal walls are still the pattern of choice in much of Greece and most certainly Mallorca, home of Artifex Balear – a stonemasonry and stone carving school, who’s director Miguel Ramis explains that “in general Mallorcan walls, are comprised of pentagonal and/or hexagonal shaped stones. In rural walls stones are usually placed in the wall as they are found, with little or no shaping, so they tend to be only rudimentary pentagons or hexagons. In more urban or formal settings the stones tend to be tailored polygonal shapes”.

These more tailored walls can be similar in appearance to the Delphi wall, degrees of tightness will vary depending on the amount of dressing employed. At the other end of the scale are the agricultural “marges” or retaining walls which terrace the slopes of the island,. As is often the case with Mediterranean limestone walls gappiness is often a bonus in providing a home for snails, often a staple of the local diet during times of hardness. These walls are similar in appearance to this one on Corfu.

Retaining wall, Paleokastritsa, Corfu. © S.Adcock

Dr.Ramis describes these as “a complex mesh of many interwoven arches”. Take a second look at the Corfu wall and you can now trace arches everywhere. Dr.Ramis further explains that “in a well built marge, most stones are surmounted by an irregular arch of other stones – and are themselves elements in one or more other arches.”

“With rectangular coursed stonemasonry, if a stone is taken out of the wall, a natural corbelled arch is formed by the stones in the courses above it. With polygonal masonry, what you get is a true arch formed by 3 or more stones. The wall would not even notice the missing stone since the arch will be in tension. Because the ground under a wall tends to subside here and there over time, especially after heavy rains, the arches embodied in the wall enter into tension. Hence a polygonal wall can withstand these movements better than a rectilinear wall due to its inherent tensile strength.

In a polygonal wall “the stones are placed vertically instead of horizontally. In the event of the foundation sinking, the stones adjust, find new positions, obey gravity, work like wedges; tensile strength is not lost. In a horizontally coursed wall, a subsiding foundation immediately causes a loss of tensile strength that can never be regained.”

“The arch is one of the strongest and most efficient building forms of all times, so it is not surprising to find they are integral to this walling system…. It is no wonder that in… areas subject to earthquake, a polygonal wall system evolved.”

This argument has a certain logic, and it seems to work, but I maintain a degree of scepticism; it seems perhaps a little too simplistic. It seems possible that the arches work as much by accident as design. It is also likely that where problems occur then they are likely to be big, to some degree the overall strength is more reliant on the interaction of everything else than in a rectilinear wall, and its perceived strength could in fact be a weakness.

Single boulder walls work in a similar way to the innate arch argument. This photo of a single boulder dyke in Strathrusdale near Dingwall shows what can happen. An arch has formed and the wall stands. But it serves no

Single, boulder dyke, Strathrusdale, Ross & Cromarty, Scotland. © S.Adcock

function. As a free standing wall it is not stockproof. If it was a retaining wall it would retain little. This is a problem of differential settlement similar to that discussed for complete bands of throughs in “Stonechat 12”. If the wall were rectilinear and well constructed then as it settled the stones would be locked in place, in this respect the formation of effective arches during settlement could be leading to loosening of stones below the arch, effectively weakening the wall rather than strengthening it.

Unfortunately none of this deals with how to actually build polygonal walls. Dr. Ramis includes details on placing hearting, the use of throughstones, straight and concave batters (a la Cornish hedge, and something Francis Menotti also notes) etc. These are principles which apply to all dry stone structures in general, but as with many such articles I`m left wondering but how the actual process is carried out.

In addition getting such a tight face has always left me wondering exactly what is going on inside. Dr. Ramis makes the succinct observation that “the front face of the stone, the one that is seen on the outer surface of the wall, should NOT be the largest face.” Unfortunately a photo of a cross section of a collapsed wall, built of highly dressed stone suggests this is not always the case. When I saw the walls at Delphi I wondered about, the extent to which the stones had been stood on edge. Does the amazing fit and hence tightness of the face, create such frictional forces that other weaknesses are at least partly negated? I then started to wonder on how well the stones fit together 3 dimensionally; after all you can fit two triangular cross-sections very tightly on the outside face without there being any contact between the stones within the wall.

Menotti (p.35) shows 8 cross sectional methods of construction (after a classification by Agurto Calvo) some of which relate to specific wall styles, others can be used in a variety of styles. One crosssection shows wedging and pinning (probably the more rustic faces), several show the stones apparently shaped in 3 dimensions notably in the encased style. In others with similar shaping the stones are fascinatingly dowelled (i.e. mortice and tenon dips and protuberances similar to the Stonehenge trilithons, many ancient Greek columns inter alia) and there is one fascinating variation identified as “braced” where a large stone on one course and the large stone on the subsequent course, have mirrored hollows, which fit over a smaller stone, in effect `pegging` the stones together (once again as with many Greek columns).

But how did they shape these stones so well to ensure a 2-D let alone 3-D fit. Menotti refers to Protzen and his experiments showing how the boulders were worked using hammerstones. Protzen is generally recognised as the leading expert on ancient methods of working stone, I remember him demonstrating the technique in the BBC TV series “Secrets of Lost Empires”. I was singly unconvinced as to how adjacent stones (especially large ones) were shaped and fitted, and Protzen has undeniably created impressive looking Inca style stonework. However having seen some of Menotti`s photos I now wonder about the more intricately shaped ones, such as the one below which is truly phenomenal, although you cannot but wonder why.

Meanwhile such jointing creates even more questions regarding 3-D fitting.

The perfection of Inca stonemasonry. Encased style jointing, Inka
Roq’e’s Palace. © F.Menotti

Protzen`s theory as to how the fits were achieved essentially relies on trial and error. I’m at a loss to come up with anything better, but it seems so unsatisfactory especially when working with really intricate shapes or enormous boulders.

Another cross-section identified by Calvo/Menotti is `denticulated` (possibly losing something in translation) where the stones only really touch at their faces, (as I had first wondered when I saw the walls at Delphi) and only requires 2 dimensional accuracy.

It still however does not explain how they withstand earthquakes. As usual there seem to be more questions than answers. Perhaps one day I`ll have a go at working it out.

It’s not really a method you come across in this country. The best approximations I’ve come across are at Wasdale Head in the Lake District, as shown, below. A distinction has to be drawn between these walls and those that are polygonal by mistake with stones just placed higgledy-piggledy, loose and pinned. Sadly some of these walls on a farm owned by the National Trust have been `gapped` in a more traditional manner, with stones laid incongruously level.

Right, Upper Wasdale,
Cumbria. © S Adcock

Dr Ramis makes the keen observation that “Spatial visualisation is an essential tool of the stonemason and something that every stonemason needs to develop”. So very true, perhaps even more so with polygonal walls, but then again maybe it’s just a slightly different form of visualisation. Perhaps one day I`ll find out, maybe by reciprocating the National Trust`s `mistake` in Wasdale by gapping polygonally in Nant Ffrancon. Watch this space!!

– Sean Adcock

Dr. Ramis` quotes are taken extensively from “Dry Stone Walls of Mallorca” an article which appeared in Stonexus VIII (pp55-60). Stonexus is the periodical publication of the Stone Foundation and I am indebted to it`s editor Tomas Lipps and Dr. Ramis for permission to use this material. I am also indebted to Francois Menotti for his kind permission to use his Inka photos. All other photos were taken by the author.

Dr.Ramis describes these as “a complex mesh of many interwoven arches”. Take a second look at the Corfu wall and you can now trace arches everywhere. Dr.Ramis further explains that “in a well built marge, most stones are surmounted by an irregular arch of other stones – and are themselves elements in one or more other arches.”

“With rectangular coursed stonemasonry, if a stone is taken out of the wall, a natural corbelled arch is formed by the stones in the courses above it. With polygonal masonry, what you get is a true arch formed by 3 or more stones. The wall would not even notice the missing stone since the arch will be in tension. Because the ground under a wall tends to subside here and there over time, especially after heavy rains, the arches embodied in the wall enter into tension. Hence a polygonal wall can withstand these movements better than a rectilinear wall due to its inherent tensile strength.

In a polygonal wall “the stones are placed vertically instead of horizontally. In the event of the foundation sinking, the stones adjust, find new positions, obey gravity, work like wedges; tensile strength is not lost. In a horizontally coursed wall, a subsiding foundation immediately causes a loss of tensile strength that can never be regained.”

“The arch is one of the strongest and most efficient building forms of all times, so it is not surprising to find they are integral to this walling system…. It is no wonder that in… areas subject to earthquake, a polygonal wall system evolved.”

This argument has a certain logic, and it seems to work, but I maintain a degree of scepticism; it seems perhaps a little too simplistic. It seems possible that the arches work as much by accident as design. It is also likely that where problems occur then they are likely to be big, to some degree the overall strength is more reliant on the interaction of everything else than in a rectilinear wall, and its perceived strength could in fact be a weakness.

Single boulder walls work in a similar way to the innate arch argument. This photo of a single boulder dyke in Strathrusdale near Dingwall shows what can happen. An arch has formed and the wall stands. But it serves no

Single, boulder dyke, Strathrusdale, Ross & Cromarty, Scotland. © S.Adcock

function. As a free standing wall it is not stockproof. If it was a retaining wall it would retain little. This is a problem of differential settlement similar to that discussed for complete bands of throughs in “Stonechat 12”. If the wall were rectilinear and well constructed then as it settled the stones would be locked in place, in this respect the formation of effective arches during settlement could be leading to loosening of stones below the arch, effectively weakening the wall rather than strengthening it.

Unfortunately none of this deals with how to actually build polygonal walls. Dr. Ramis includes details on placing hearting, the use of throughstones, straight and concave batters (a la Cornish hedge, and something Francis Menotti also notes) etc. These are principles which apply to all dry stone structures in general, but as with many such articles I`m left wondering but how the actual process is carried out.

In addition getting such a tight face has always left me wondering exactly what is going on inside. Dr. Ramis makes the succinct observation that “the front face of the stone, the one that is seen on the outer surface of the wall, should NOT be the largest face.” Unfortunately a photo of a cross section of a collapsed wall, built of highly dressed stone suggests this is not always the case. When I saw the walls at Delphi I wondered about, the extent to which the stones had been stood on edge. Does the amazing fit and hence tightness of the face, create such frictional forces that other weaknesses are at least partly negated? I then started to wonder on how well the stones fit together 3 dimensionally; after all you can fit two triangular cross-sections very tightly on the outside face without there being any contact between the stones within the wall.

Menotti (p.35) shows 8 cross sectional methods of construction (after a classification by Agurto Calvo) some of which relate to specific wall styles, others can be used in a variety of styles. One crosssection shows wedging and pinning (probably the more rustic faces), several show the stones apparently shaped in 3 dimensions notably in the encased style. In others with similar shaping the stones are fascinatingly dowelled (i.e. mortice and tenon dips and protuberances similar to the Stonehenge trilithons, many ancient Greek columns inter alia) and there is one fascinating variation identified as “braced” where a large stone on one course and the large stone on the subsequent course, have mirrored hollows, which fit over a smaller stone, in effect `pegging` the stones together (once again as with many Greek columns).

But how did they shape these stones so well to ensure a 2-D let alone 3-D fit. Menotti refers to Protzen and his experiments showing how the boulders were worked using hammerstones. Protzen is generally recognised as the leading expert on ancient methods of working stone, I remember him demonstrating the technique in the BBC TV series “Secrets of Lost Empires”. I was singly unconvinced as to how adjacent stones (especially large ones) were shaped and fitted, and Protzen has undeniably created impressive looking Inca style stonework. However having seen some of Menotti`s photos I now wonder about the more intricately shaped ones, such as the one below which is truly phenomenal, although you cannot but wonder why.

Meanwhile such jointing creates even more questions regarding 3-D fitting.

The perfection of Inca stonemasonry. Encased style jointing, Inka
Roq’e’s Palace. © F.Menotti

Protzen`s theory as to how the fits were achieved essentially relies on trial and error. I’m at a loss to come up with anything better, but it seems so unsatisfactory especially when working with really intricate shapes or enormous boulders.

Another cross-section identified by Calvo/Menotti is `denticulated` (possibly losing something in translation) where the stones only really touch at their faces, (as I had first wondered when I saw the walls at Delphi) and only requires 2 dimensional accuracy.

It still however does not explain how they withstand earthquakes. As usual there seem to be more questions than answers. Perhaps one day I`ll have a go at working it out.

It’s not really a method you come across in this country. The best approximations I’ve come across are at Wasdale Head in the Lake District, as shown, below. A distinction has to be drawn between these walls and those that are polygonal by mistake with stones just placed higgledy-piggledy, loose and pinned. Sadly some of these walls on a farm owned by the National Trust have been `gapped` in a more traditional manner, with stones laid incongruously level.

Right, Upper Wasdale,
Cumbria. © S Adcock

Dr Ramis makes the keen observation that “Spatial visualisation is an essential tool of the stonemason and something that every stonemason needs to develop”. So very true, perhaps even more so with polygonal walls, but then again maybe it’s just a slightly different form of visualisation. Perhaps one day I`ll find out, maybe by reciprocating the National Trust`s `mistake` in Wasdale by gapping polygonally in Nant Ffrancon. Watch this space!!

– Sean Adcock

Dr. Ramis` quotes are taken extensively from “Dry Stone Walls of Mallorca” an article which appeared in Stonexus VIII (pp55-60). Stonexus is the periodical publication of the Stone Foundation and I am indebted to it`s editor Tomas Lipps and Dr. Ramis for permission to use this material. I am also indebted to Francois Menotti for his kind permission to use his Inka photos. All other photos were taken by the author.