www.cheops-pyramide.ch Copyright 2006 Franz Löhner and Teresa Zuberbühler

The outer stones (casing)

A new method by Franz Löhner

A special visual impact was created by using white outer Tura stones. Franz Löhner postulates, that these outer stones were an integral part of the pyramid and not only a mantle or shell added.
Importance of outer stones - Procedure - The Tura stone - Stone dressing on the pyramid plateau? - Stone bond patterns - Laying the outer stones - Jointing and polishing - Polishing from the top down? - Special stones - Hiding the entrance - Khafre's Pyramid - Mantle or integral part? - Stone courses - Sources

Importance of the outer stones

At the moment, when the construction of the pyramid was finished, the surface of the pyramid presented an immaculate, even, plane and steep surface with no entrances and no possibility to climb up. The white Tura stone, the builders had chosen for the outer stones must have been dazzling. To produce this visual impact, the surface of the pyramid had to be unblemished, seamless and very smooth.

To achieve this, all joints between the stones had to be as small as possible and filled with mortar, so they were nearly invisible. This was done with an impressive precision as can be observed on the lower courses of the pyramid of Khufu, where not even a knife can be slid into the crevasses between the stones.

It was very important, that the outer surface should not shift, crack or even fall down in pieces. So not only the layer of stones at the outside, but the next inner layers had to planned precisely as well. The outer Tura stones were layed in such a pattern, that the stones would interlock and the masonry would be tied together with long header (or bond) stones. If core stones should shift and change their position, this would have been seen on the outside, because the surface would crack and the intended visual impression of smoothness and perfection would be destroyed.
Photo of the outer casing of the step pyramid of Saqqara, which has moved and is flaking off

The fact, that even in the 12th century most of the outer surface stones still existed (observed by Abd al-Latif) shows, how lasting and admirable the Egyptian architectures built. The beautiful outer stones were very popular and were removed from the pyramids bit by bit and used as building material for mosques and houses in Cairo. But even in 1639 the Oxford astronomy professor John Greaves wrote, that the whole face of Khafre's pyramid except the southern side was still entirely intact, but at that time the stones of the pyramid of Khufu had already been removed [5].

Procedure of laying and polishing the outer stones

The pyramid building yard - the center of the construction project
Transporting the pyramidion to the top of the pyramid

The Tura stone

The outer stone layer of the pyramid of Khufu was built with Tura stones. This is a specially beautiful white limestone and is quarried in Tura, which lies to the southeast of Giza on the other side of the Nile. Tura limestone is quite soft und can be worked easily but after being exposed to air for some time it hardens. The stone was very much treasured by the ancient Egyptians, it was used for several pyramids, for other monuments and for statues as well. The Arabs also liked this stone and used it to build mosques. For this purpose a lot of stones were removed from the pyramids.
Quarrying stones for the pyramid (more information about Tura)

Dressing the stones on the top of the pyramid plateau?

Accepted doctrine says, that the stones were dressed and bevelled on top of the pyramid plateau. That is absurd, because there are no good reasons, why this should be done there - why should the builders tediously determine the inclination of the pyramid flank stone by stone? On the contrary, it is important, that the stones are dressed and bevelled already in the quarries and not on the plateau. To achieve the exactness necessary, specially for the outer stones, where the angle should be the same at all times, you need enough working space to dress the stone. On the pyramid plateau which gets smaller and smaller as work progresses, this is not possible.
Quarrying stones for the pyramid (dressing the stone)

As the building work progressed, the plateau became progressively smaller, reducing the working area - just hauling the stones to their intended place, laying them there and polishing the outer stones was already difficult enough!
Illustration dressing the stones according to the Egyptologists

Can the necessary precision be achieved?
Definitely - this is actually much more feasible if you do it in the quarries than if you dress and bevell the stones on the pyramid plateau.
First - the neighboring stones are cleaved in the quarry from the same layer of rock. With this method where you split the stones along their cleavage plane, the break is even and you don't have to rework the stone a lot, so they fit flush to each other. With this method you produce stones with a varied edge and an edge of the same length. Stones that were cut from the same piece of rock are also layed down as neighboring stones on the pyramid. In the quarry they can already be layed down next to each other to see if they fit and if necessary they can be made to match.
Second - here in the quarry a complicated corner stone can be made exactly to measure and with the precise angles it should have.
And last - why haul a heavy stone up the pyramid only to cut off a large part and to carry the stone chips back down? Don't forget - the old Egyptians were down-to-earth and wouldn't waste their resources!
Quarrying stones for the pyramid (working stones in Tura)

There definitely wasn't a building yard on top of the pyramid plateau - and by no means a smithy was erected there - the heat of the smiths fire would have damaged and cracked all stones lying underneath!

W. Petrie has establish [6], that the layers of the pyramid of Khufu are of different heights. Generally the lower courses are higher and the ones at the top smaller, but again and again there are exceptions, where several layers are higher than the ones before. For example the 19th layer is suddenly thicker and between the 35th and the 49th layer there are again thicker layers of stone.
Stone courses of the Pyramid of Khufu

Measurments of the stone courses also show, that again and again there are stone layers where the thickness vary only about 1-2cm. Franz Löhner thinks, that this proves, that the stones of one layer were cut from the same rock layer or sheet (bed) in the quarry and then, if possible, layed down on the pyramid close to each other. If you use a ramp it is specially important, to use smaller blocks for each higher course, because the ramp gets smaller and steeper towards the top. You don't have this problem, if you use Löhner's rope rolls. These thicker stone layers are a strong argument against ramps and for Löhner's methods!

Stone bond patterns

Stones can be stacked or laid up in a variety of bonds or patterns, to build walls or other structures. The stones should be arranged in such a way as to provide strength and stability in a masonry structure. Bonding is required to strengthen and stabilize a wall and enable it to carry vertical and horizontal loads.

To accomplish this so called headers are used, which are long stones reaching into the masonry structure and tying together the shorter stones around them. For example in the Flemish bond alternate stretchers (= laid lengthwise) and headers (laid crosswise) are laid in a course (illustration).

The ancient Egyptians chose even more complicated bonds. They used angular joints and stones shaped like a trapeze to be sure, that the structure was safe from tension and the formation of cracks. Irregular corner joints and interlocked joints also helped [3]. We know, that they also always left some stones from one course protruding up into the next course, only for a few centimeters, but that was enough to achieve more stability [2].

W. Petrie [6] thinks, that the stones lying in the very middle and at the extreme corner of each course of blocks of the pyramid were layed down specially carefully and then those stones would provide a guide to ensure the geometrical accuracy of the four right angled corners and the outer stones between. Specially large and long stone blocks, so called headers were layed in the middle, so they were well interlocked with the other stones. Because these stones are missing nowadays, removed for buildings in Cairo, there is a slight indentation and the pyramid sides seem to be slightly concave.

Laying the outer stones

Franz Löhner thinks, that the outer stones - he doesn't use the term "casing", "outer shell" or "pyramid mantle" - were layed down and set at the same time as the inner stones and that they were interlocked with those stones for more stability. Because nowadays the inner stones can be seen, you can observe, that the outer stones are wedged between the inner stones. So called headers were put down, reaching into the inner core of the pyramid.

The outer stones were ordered to measure in the Tura quarries, cut exactly, bevelled and delivered according to an exact plan. The jointing, if done well, needs some preparatory work, the stone masons have to know where a particular stone will be layed and they have to know the neighboring stones. If you put a block just anywhere, tensions in the building can result and stones can crack and break. Actually the whole pyramid of Khufu seems to have set a couple centimeters over the last thousand years. The stones had to be dressed according to a position plan, then marked (graffiti illustration), stored at the foot of the pyramid if not used immediately, and then transported to the construction site in a certain sequence and layed at its designated place.
The pyramid building yard - the center of the construction project

Jointing and polishing the outer stones

Two variations of mortar were used in the pyramid of Khufu. The outer stones were joined with an extremely thin gypsum mortar which hardens cement-like [1]. For the inner core stones a mixture of gypsum, lime and sand was used. Illustration joints western side.

In the first layers of the pyramid several thousand stones were layed and only a few hundred outer (casing) stones of Tura limestone. The smoothing (not dressing) of the outer stones could be done during the time the inner stones were layed down. To do this, a working platform was attached with two ropes from the slant, so the polishing and grinding could be done with ease. For polishing fine quartz sand mixed with water was used.

Franz Löhner thinks that a team of 20 polishers could smooth a surface of 1.5m² per day. This is about the surface of one standard outer casing stone.
Detailed calculations how many workers were necessary to build the pyramid

Polishing from the top down?

Egyptologists propose, that the outer stones were bevelled and polished as follows (accepted doctrine [5]):
The Tura-stone is delivered from the quarry with only the bottom dressed. It is hauled to its intended place on the pyramid. Now the side joint faces of the stone are dressed so they fit the neighbouring stone. The slope is marked on the joint face. The stone is moved to lie flush to its neighbor stone and the rollers are removed. Now the upper face is leveled (illustration left - the yellow part still has to be removed). Part of the stone is still overhanging the stone course beneath. Where the two neighboring stones touch each other extra stock on the front of the block is bevelled away from the slope line . Now there are two variations how to proceed. In some scenario all the outer stones are bevelled before the next stone layer is put on top. But most Egyptologists propose, that the stones are left like this because they help to anchor the ramps. Only once the pyramidion is put on top and the ramps are demolished, the stones are bevelled, dressed and polished from the top down (as written in Herodotus Book II).

With these methods it is not possible to achieve an even surface or the desired accuracy! On the contrary, when beveling the upper stones, the strong blows would be transmitted through frictional connection to the stone lying underneath and that stone could break or crack. Franz Löhner thinks, that the Tura stones were dressed and bevelled as accurately as possible already in the quarries and then were brought to the pyramid. Here they were hauled to their intended place placed next to their neighboring stone and then had to be polished to be finished.

The reason why Egyptologists think, it was done as described above is, because they all think, the pyramids could only be build with the help of ramps. To anchor a ramp to the pyramid body you have to leave the outer stones in such a way, that they protrude into the ramp. On a smooth outer surface the ramp would start to slide down immediately. But with ramps you can't dress and polish the surface straight away, you first have to dismantle and remove the ramps to reach the surface. But even this is not so easy. Ramps cover most or large parts of the pyramid, but never the less there are several places on the flank that are not reached directly by a ramp. So to trim the pyramid face from extra stock and polish the surface, additional smaller ramps or scaffolds have to be built. This is a serious flaw of all ramp models. You don't only have to build a huge building - the pyramid - but with nearly as much effort you build a ramp and then you have to dismantle it again at the end! With Franz Löhner's methods the pyramid is practically finished at the moment the pyramidion is put on top the pyramid, the whole surface is already smoothed and polished, and all you have to do, is to remove the protruding parts of the special Tura stones used for anchoring the last track.

Check measurements
If you bevell and polish the stones from the top down it is very difficult to achieve the desired precision. The inclination of the lateral surface has to be exactly 51.84°. According to Franz Löhner this angle is already measured as exact as possible in the quarry and then again controlled at the building yard at the foot of the pyramid with the help of a special wooden gauge. When the stones have arrived at the required height, the outer stones are placed on top of each other and the angle and the exact fit is checked again. By placing a wooden plank on top of the surface you can also control, if the surface is level or concave. The fit of the important corner stones can be controlled by stretching a rope along the pyramid ridge (or by placing a plank on top). After finishing each stone course the surface of the pyramid frustum is measured, the corners checked if they measure exactly 90 degrees and if the length of the four edges are the same. If mistakes are found, they can still be corrected, either by replacing a stone or by cutting it to a better shape.

Imagine, how those errors in measurement would add to each other, if no check measurements can be made! But this the case, if you just put down roughly cut stones on the outside edges - while the building is going on neither the right angles at the corners nor the length of the four edges of the pyramid frustum can be checked. Then towards the end, when you start to bevell and polish the outer stones from the top down, it is quite easily possible to get slightly different angled stones, since the stones can't be canted and not all sides of the stone can be measured. Franz Löhner thinks that in the quarry a series of very accurate stones were made. Then they are controlled again by putting them next to each other and if necessary they are changed again and only now they are transported to the pyramid. When they arrived there, each stone was part of an immense three-dimensional puzzle which fitted exactly to the neighbouring stone to the left and right, the stone underneath and if necessary also above!
Theories of pyramid ramp systems disproved
Ramp models described in details
Transporting the pyramidion to the top of the pyramid

Special stones

The volume of the casing stones is about 5% of the entire volume of the pyramid and would form a cube with a length of 50m. Most of the Tura stones were standard stones for the lateral surface - they were made to measure but in their shape they were similar. Additionally special stones had to be cut, for example the corner stones. The shape of these stones had to be planned exactly and their execution was very time-consuming.
Detailed calculations how many workers were necessary to build the pyramid
The pyramid building yard - the center of the construction project

Stones for anchoring the track system
According to Franz Löhner's methods the rope roll stations and tracks had to be anchored to the outer casing stones. Therefore these stones had to have a special shape and reach specially far into the core masonry.

Some outer Tura stones with a special form are left protruding every 30-37m. They are angled up in such a way, that the rope rolls can be laid atop and then tied down either with ropes or with a wooden casing (ropes are not shown on this illustration). They have to be specially well interlocked with the wall to distribute the load. A slit is chiseled into the stone just underneath the rope roll, so the rope can be directed down to the sledge. Illustration alternative how the achoring stone could look like.
Transport up the pyramid flank with Löhner's rope roll

Pyramidion
The uppermost piece or capstone of a pyramid is called "pyramidion" (plural pyramidia). The pyramidion of a large pyramid such as the pyramid of Khufu weighted around 5 to 6 tons, was made from Tura limestone, granite or diorite and was perhaps gold plated [2]. This stone had to be cut to measure (taking into account, that slight errors in measurement might have occurred and the top of the pyramid was not exactly centered), specially burnished and polished.
Transporting the pyramidion to the top of the pyramid

Hiding the entrance to the pyramid of Khufu

It is not known, if a corpse was ever buried inside the pyramid of Khufu. So it is also not clear, if the entrance to the pyramid was closed when the pharaoh Khufu died or if closing the passage was done during the construction or later after the pyramid was finished building.

Massive stones of the entrance passage of the pyramid of Khufu [2] as seen today

The entrance or - if we take the view of the pharaoh - the exit of the pyramid of Khufu doesn't lie in the exact middle of the northern pyramid flank but is offset by 7.29m to the east on used to be on 16.76m [6] height (19th course- a specially thick stone layer), today it is at 13.71m (16th course) and several meters back from the pyramid face . It was entirely covered with Tura casing blocks, until those blocks were taken away for the purpose of building houses in Cairo.

The exact point in time when the actual entrance was found is not clear. There is an entrance underneath, probably cut by grave robbers but perhaps the caliph Abd Allah al-Mamun forced his way into the pyramid in 820 AD. It is interesting, that the tunnel connects directly to the descending corridor, circumventing the large granite stones blocking the way in. This could signify, that somebody dug the tunnel, who knew quite well about the system of passages inside the pyramid. Probably the caliph only enlarged the tunnel. Photo entrance to the pyramid of Khufu / Photo 2 / Illustration

Outer casing stones of Khafre's pyramid

Khafre's pyramid has still most of its outer stones in place on the top. Part of the "casing" seems to hang in midair since centuries, because the lower stones were removed. Even in 1639 the British John Greaves wrote, that the outer casing stones of Khafre's pyramid were intact except on the southern face [5]. This shows, that the ancient Egyptians interlocked the outer stones most thoroughly with the inner stones.

The outer surface of Khafre's pyramid can be divided into three parts - on the very top there are intact Tura stones (about 70 to 90 stone courses) which then abruptly break off, then an area which lies like a belt just underneath the Tura stones where the outer stones are missing. Not only the Tura stones but approximately three stone layers lying just underneath are also missing. This can seen specially well at the northeastern corner, where the ridge brakes off vertically. Under this belt there is a third area where the stones are rougher and irregularly cut off. A possible explanation could be, that the entire area just underneath the intact surface slid down all at once when too many of the supporting stones underneath were quarried or for example during a earth quake.

You would expect, that a pyramid would be constructed with thick stoneslayers at the bottom and thin courses at the top. Bit it is interesting to notice, that again and again there are thicker stone courses, some quite high up on the pyramid. This fact was also noticed at Khufu's pyramid.
Stone courses of the Pyramid of Khufu

Mantle or integral part?

To build a slope, different techniques can be used. Existing masonry can be trimmed, you bevell off the protruding parts of the stones and get a slope. Or you can add a casing to the core masonry, and obtain a slope like that. Here the term "mantle" can be used, because the stones are only added after finishing the whole building. Or you can plan the building, so stones integrated into the masonry form a slope. All stones are bevelled to a precise angle and layed down in such a way, that they are interlocked with the other stones and anchored.

Franz Löhner thinks, that the outer casing stones were transported up Khufu's pyramid and put in their intended place at the same time as the stones for the core and then were burnished and polished. The outer Tura stones were an integral part of the pyramid structure, that is to say they were interlocked and bonded with the core stones and not used to encase the structure like a mantle or skin. (The following illustrations are not drawn to the same scale)

In literature about the pyramids you still find illustrations of the pyramid of Khufu with the so called pyramid core and an outer mantle, even by people knowledgeable in Egyptian architecture [2 and 7]. According to these theories the core of the pyramid was build first (1 on the graphic) and then a mantle or outer shell (2) was added. Considering the great height of the pyramid of Khufu, we think, that if the outer stones were a shell around the inner core, then the outer shell would start sliding down, because the weight is too large and the stones are not anchored enough. This probably would have happened already while building. Anyway, a core with vertical tiers has been found neither in Khufu's nor in Khafre's pyramid. This kind of inner core should be visible at least at the top of the Khafre pyramid, where only 9 stone layers have been removed. Illustration of the upper layers of Khufu's pyramid.

An argument against an inner core is the fact, that the stone layers of the pyramid of Khufu vary only about 1-2cm in thickness. The largest differences are found in the first 15 layers where the pyramid is built around a rock outcropping and then again at the height of the ceiling of the King's chamber (course 58-59). The maximal difference is 10.9 cm in the 12th course [7]. These differences are evened to 1cm in the following stone courses. Such an accuracy is only important, if the following stone layers have to lay flush on top of the previous layer. With a pyramid core and an outer mantle this is not important - on the contrary, for better stability the small outer mantel layer should be inclined inwards - see the following example!
Stone courses of the Pyramid of Khufu

In Meidum a pyramid probably commissioned by the pharaoh Huni is located, which was possibly built using the principle of core and mantle. The pyramid was initially executed as a pyramid with 7 steps, but perhaps even before it was finished, an eighth step was added. Then the pharaoh Sneferu continued to change the shape of the pyramid, probably intending to build a true, smooth sided pyramid [4]. While the stones of the original steps were tilted inwardly, the outer mantle was build with horizontal stone layers [5]. A theory suggests, that already during construction the outer stones slipped and parts of the inner steps collapsed. The inner core of the pyramid still stands but is surrounded by a mountain of rubble. In Zawiyet el-Aryan lies an other pyramid - now only a stump - which was also built with a core and a mantle.

There is also evidence of structural problems in the Bent pyramid, as can be observed in the entrance passage, where a 23cm high step is found (photo). Here the exterior mantle was dislocated from the core because the outer stones were not interlocked well enough with the core stones.

This pyramid was first planned and executed with a steep angle of inclination, then the ground beneath the pyramid gave way. The builders lengthened the base and a new angle was chosen. Because this didn't solve the structural problems, the angle was drastically reduced which resulted in much less overall height. The fact is, that the builders eventually solved the problems, because the pyramid still stands after several thousand years and the outer flank still hasn't yet slipped, even after the corner stones were removed.
Alignment of the pyramids and controlling the shape of the pyramid

Photos Khafre / Bent pyramid - Patches on the outer pyramid flank / Zawiyet el-Aryan / Meidum

Additional information about the stone courses of the pyramid of Khufu

• Illustration of the courses of the pyramid of Khufu - the lower 50 stone tiers [6]
• 1. course 1.46-1.49m / 2. course 1.25-1.33m / 3. course 1.15-1.22m / 4. course 1.11-1.13m / 5. course 0.99-1.03m / 6. course 0.97-1.06m / 7. course 0.99-1.12m / 8. course 0.89-0.96m / 9. course 0.87-0.93m / 10. course 0.82-0.96m [2]
• Thick stone courses (more than 90cm high, the thinnest stones courses are 51.5cm high): 1 to 10 / 19 / 35 to 38 / 44 to 45 / 47 to 48 / 90 to 91 / 98 to 100 / 118 / 201 [3]
• The whole pyramid consisted of 210 stone courses, and even just underneath the apex (tip) on the 201st course, large and heavy stones (1.12m = 2 Ellen) were used [4]. This fact strongly speaks against the use of transport ramps, because with those it is imperative that towards the top only smaller stones are hauled up the ramp, since it is getting much smaller there.
• Average height of the stone blocks is 0.69m, the height most commonly used was 0,60m = 8 palm [3]

Sources

[1] V. Maragioglio und C. Rinaldi Architettura delle Piramidi Menfite. Le grande piramide di Cheope
[2] D. Arnold Building in Egypt
[3] G. Goyon Die Cheops-Pyramide
[4] R. Stadelmann Die grossen Pyramiden von Giza
[5] M. Lehner Geheimnis der Pyramiden
[6] W. Petrie The Pyramids and Temples of Gizeh
[7] L. Borchardt Einiges zur dritten Bauperiode der grossen Pyramide bei Gise

www.cheops-pyramide.ch Copyright 2006 Franz Löhner and Teresa Zuberbühler