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The mighty pyramid of Khafre was the second largest pyramid constructed in ancient Egypt,
yet few scientific investigations have taken place there.
The messy condition of the exposed core makes analyzing the structure extremely challenging.
By comparison, the Great Pyramid is much safer to climb and easier to measure and so the
height of each course has been well-documented by multiple explorers.
These surveys have led to interesting observations, such as the courses decreasing in height as
you go up the pyramid, only to periodically reset with an exceptionally thick course.
Some of these larger courses align with interior features of the pyramid, such as second tallest
course number 35 marking the ceiling of the Queen’s Chamber.
But with so much of Khafre’s pyramid masonry left in disarray, it isn’t even known how
many courses of stone the pyramid was originally constructed with.
Only the upper sections of the pyramid are in a measurable condition, but so far nobody
has risen to the challenge of doing so.
Thus, the most precious section of Khafre’s pyramid remains mostly out of sight because
of the difficulty posed in conducting the survey.
The remaining casing stones at the summit look precarious, as if one more earthquake
might cause this final section to come crashing down all at once.
At the very least, the Ministry of Antiquities has added some reinforcement to protect the
most vulnerable stones from falling off the pyramid.
The tall and squared vertical supports are modern additions placed under areas where
original blocks were overhanging.
Additionally, the outlying square blocks on the northeast corner are modern additions
as well, probably to help workers climb to the bottom of the casing stones to do the
repair work.
It’s only been in the last decade that drones have enabled a close look at the top of pyramid,
and it’s amazing to see how few courses are missing from the top as it was constructed
thousands of years ago.
Seeing it up close transports you back in time to marvel at the achievement as it would
have been viewed in its original glory.
Recently as I was watching this particularly beautiful shot swinging over the apex and
down the western face of the pyramid, a crazy thought entered my mind.
It occurred to me that I possessed enough detailed imagery of Khafre’s casing stones
that maybe I could map out their arrangement for the very first time.
Analyzing the original casing stone layout could reveal clues about how the pyramid was
originally constructed, and it’s a shame nobody in Egyptology has ever bothered to
study this.
I’m guessing the difficulty of the task combined with the uncertainty of making a
discovery has dissuaded anyone with access who might have considered conducting this
investigation.
That attitude is a far cry from the accomplishments of early explorers such as Flinders Petrie,
who recorded every pyramid measurement within his means.
He made those surveys for their own posterity, not knowing if the rigorous work involved
was likely to lead to a big discovery.
Perhaps someday advances in technology will make a casing stone study easier to accomplish,
but so far there’s no shortcut to mapping them out.
Even high-end photogrammetry such as this 8k resolution scan done by the World Scan
Project is not adequate by itself.
With that said, I’d love to use photogrammetry as tool for presenting on the pyramids, but
I haven’t been able to get in touch with anyone who can provide access.
Perhaps a kind viewer can help me out here.
My solution for mapping the casing stones was to find the straightest angle possible
on each side, and use close-up drone flybys as a reference to outline each casing stone
on the wide shot.
There are many casing stones which contain cracks or degradation and some are entirely
missing.
You need a very close look to be confident you’re not mistaking damage for original
joints.
Also, some joints remain so tight that they are difficult to spot at all.
I had to accept this work would not be perfect, but if you’re going to study ancient history
you can never let perfect be the enemy of good.
After spending a lot of time up high, what was once so foreign began to feel familiar.
You start to notice patterns, such as the south face having dramatically more water
streaks on the casing.
I’m not sure if this is due to the direction wind-blown rain falls at Giza, or if perhaps
the pyramid is tilted slightly southward which causes more water to drain in that direction.
My mapping project began on the western face, which was the side I could see the clearest
but also happens to be where the casing stones are most damaged.
This was probably the best place to begin, because I could train my eyes on damaged areas
without the bias of looking for previously discovered patterns.
It was quickly apparent I only had enough detail to map the upper 30% of the remaining
casing stones.
The uppermost courses are all about 1 cubit tall, equal to 52.5 centimeters.
Starting from the top, you don’t encounter a dramatically tall layer until you reach
courses 46 and 47.
These tall courses are conspicuously well-preserved on all four sides of the pyramid, and so they
served as a natural boundary for the range of my survey.
Perhaps these highest large courses functioned as a refoundation of the pyramid for its final
stage towards completion.
When triangulating the missing courses at the top of Khafre’s pyramid, I calculated
2.5 meters of stone is missing above the highest remaining block.
In my previous video about casing stones, I erroneously said 7 meters was missing, as
cited from Wikipedia.
That number was clearly just made up, probably because nobody has ever conducted a proper
survey at the top of Khafre’s pyramid.
With 2.5 meters of stone, you could hypothetically have 5 courses missing, each a little under
1 cubit in height.
The closest example of a surviving capstone of a satellite pyramid next to the Great Pyramid
follows those proportions.
But a pyramidion that small seemed too dainty for the second largest pyramid of Egypt, so
I opted to give the capstone about 1 meter of height covering what would otherwise be
2 courses.
This felt like a good compromise between the tiny local pyramidion, and the largest recovered
pyramidion of Amenemhat III made over 600 year later at 1.4 meters tall.
This means I’m counting 4 courses of stone missing at the top of Khafre’s pyramid,
and course 5 begins with the highest remaining block.
At the Great Pyramid courses are counted starting from the bottom, but since we have no way
to accomplish that at Khafre’s pyramid I will instead be counting from the top.
When looking at my casing stone diagram, the black areas represent sections of the pyramid
which I could not map with confidence.
These areas could be comprised of multiple stones, or even include missing portions of
adjacent stones.
This doesn’t mean the black sections are only where stones are presently missing, because
sometimes damaged stones still revealed enough to see where the joints once existed.
Thus, the black sections are simply to be ignored as best you can.
And finally, it’s inevitable that a few mistakes may have slipped in.
A particularly straight and well-placed crack may have been mistaken for a joint, and an
extremely thin original joint may have not been spotted.
Generally speaking, my visibility was better at the top of the pyramid and thus the bottom
of each map is more prone to error.
So, when studying the diagram for clues, don’t get hung up over any single casing stone.
When studying the map, a pattern that immediately jumps out is the alternating layout of stones
at each corner.
These larger, rectangular blocks, have their long side on one face of the pyramid, and
the short side on an adjacent face.
The short side of a corner stone also represents the approximate depth for that course of casing
stones.
So universal was this pattern that I never deviated from it in my diagram.
However, courses 40 and below had major cracks in these stones on three corners of the pyramid,
and so if I missed an anomaly in this pattern, that’s where you might find one.
The layout for the corners of the pyramid was clearly preestablished, but the rest of
the stonework on the western face didn’t point to an obvious pattern.
A few subtle hints included longer blocks trending toward the corners in the top 25
courses, and the highest courses still containing long stones.
Course number 5 probably was down to only two blocks on each pyramid face.
I also did not detect any rule for number of stones per course, sometimes a higher course
would have more stones than the one below it, and often the same amount.
After finishing the western side, I had completed about 600 mapped sections, meaning there was
still another 1800 to go.
But you know, heh, who’s counting, right?
The south face was next, and right way something I missed earlier jumped out at me.
An interesting feature near the top of Khafre’s pyramid is that a few joints are dramatically
wider than normal.
Originally, I assumed this was due to earthquakes shaking the top loose, but the angle of the
pyramid there doesn’t shift to account for that much extra space.
Then I noticed this unprecedentedly small block and alarm bells started going off in
my mind.
Other nearby sections that could have been mistaken as crushed ends of longer stones
were actually separate thin sections of masonry.
This meant the large gaps near the top were probably original, and had been filled in
with mortar or very thin limestone blocks.
Thus, the very top of the pyramid did not have stones pre-cut to an exact size.
Or, if they had been pre-cut, the builders could not set them in place without extra
clearance on their sides.
This rougher finish at the top of the pyramid would not have been visible from the desert
floor, and this observation further supports my assertion that pyramidions of the 4th dynasty
were probably undecorated.
The south face is similar to the west in that longer blocks make up most of the highest
courses, and below them from about course 13 through 25 the stones in the center of
each face trend shorter than those near the corners.
The extra tall courses 46 and 47 at the bottom were so well preserved that I may have missed
a few hidden joints among their largest blocks.
Next came the north face of the pyramid, and I was totally blown away by what it would
reveal.
I didn’t have enough resolution to map the north face below course 43, but what I could
map was beyond impressive.
Despite the highest courses having excessive damage on this side, the north face was exceptionally
well preserved.
This allowed me to notice that the blocks here were conspicuously more homogenous than
the other faces.
In this regularity, a clear pattern emerged.
From courses 15 through 29, you had the longer blocks making up the corners and an adjacent
stone.
In the center were very similar medium-sized blocks that each overlapped one joint.
Connecting the center stones with the longer corner blocks were the smallest casing stones,
and these contained a tapered edge with the bottom of the block shorter than the top.
So persistent was this pattern, that it could not have been accidental or random.
And this clue may bring us one giant leap closer to discovering the method used for
constructing the pyramid.
My interpretation, is that the long corner stones were always laid first.
This probably helped control the angle of the pyramid in addition to making the corners
more stable.
Next, the center was filled in and because these upper courses are so short, we don’t
have multiple work stages that camouflage this regularity.
Finally, the center and the corners are bonded together with a block that is notably smaller
with an edge tapering to make its base shorter.
Perhaps the shape of this block reveals its method of insertion.
A smaller stone would be easier to lift into place from above if it couldn’t slide in
laterally.
Once the block is aligned, the tapered edge could be the final dressed side so the block
slowly sinks into place with a perfect fit.
Now I’m probably not the first person to suggest a stone with this particular shape
could be purposefully designed to fit in this way.
But there’s a huge difference between speculating the ancient Egyptians could have done this,
and my map of the casing stones which tells us that they almost certainly did.
What these small tapered blocks tell us, is where the final stone was laid on each face
of the pyramid.
This in turn might reveal a pattern that would indicate where a ramp terminated, because
you would expect that location to be the final area constructed for each course.
Complicating the matter would be if multiple ramps were used, especially if each side contained
a ramp in a symmetrical arrangement.
When highlighting these stones on all 4 sides of the pyramid, you can see that they cluster
together in vertical sections.
My methodology for identifying these blocks is that they must be much smaller than average
for their course with at least one tapered edge narrowing towards the bottom.
Because visibility isn’t perfect, there may be some small stones with subtle tapering
that were missed, and I have only highlighted ones with very high confidence.
Comparing the layout of the small tapered blocks on each face shows a somewhat similar
distribution, however the south face is the one that catches my eye.
The south face appears to have these small, tapered blocks trending towards the southwest
corner, and the few outliers that don’t follow this pattern are almost all within
a rare course has more than one of these stones.
Remove those redundancies, and you get an even stronger signal.
Adding to this evidence is that the southern face has the largest gaps between the stones
in the highest courses, suggesting this side had the most constrained working conditions.
These factors combine to suggest that the southwest side is the most likely location
for a ramp, based upon the pattern laid out by the casing stones.
This is an interesting parallel to the Great Pyramid, where the most well-conceived construction
models place an external ramp terminating in its southwest corner.
The situation is no doubt different due to the height we are observing this pattern on
Khafre’s pyramid, but the builders may have been inclined to use the south face of a pyramid
for a majority of construction access.
This also correlates to the north face of the pyramid having the most homogenous arrangement
of stones.
Before moving on, here is the east face of the pyramid in a full-frame diagram as well,
so you have the chance to spot any patterns I might have missed.
I want everyone to have the opportunity to make a discovery, and please share what you
have seen in the comments.
Clearly the next step is for an in-person survey of the casing stones at Khafre’s
pyramid.
This will allow us to remove areas of uncertainty, measure the angles of tapered joints, and
give us a perfect picture of how the pyramid was designed thousands of years ago.
Don’t forget about 70% of Khafre’s casing stones remain unmapped, and the Bent Pyramid
remains completely unmapped as well.
This video is only a first step towards that goal.
It will be challenging work up high at Khafre, and while drones are pretty good you will
need climbers to inspect the most difficult areas that may be obscured with debris.
But I think I’ve shown the work is worth doing, and that the evidence is there if we
really want to solve mysteries of the pyramids.
Surely someone is out there with the means and desire to make it happen, and now they
can move forward with confidence knowing the findings will bring us closer to understanding
how the pyramids were built.
Most importantly, this survey must be shared with the public so that we can all work together
in reconstructing our ancient history.
If I’ve learned anything about Old Kingdom pyramids, it’s that the job of decoding
them is bigger than any single person.
It's time we increased our resolution of the past so that everyone in the present can enjoy
the challenge of putting history back together, one stone at a time.
Thanks to everyone who watched this video to the end.
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