Four. Eight from the air.
Each face is slightly indented inward, visible only in low sunlight from above. Noted in 1940 on an aerial photograph; not recognizable from the ground.
The simple answer is four, plus the square base. A pyramid has four triangular faces that meet at a single apex, and nothing changes about that with this structure.
The interesting answer is eight. Because the four faces are not perfectly flat. Each one is slightly indented inward at its center, meaning it technically consists of two very shallowly sloped halves. If you count them up, that gives you eight surfaces.
The indentation is minimal. It amounts to less than one degree, which over a face length of around 200 meters results in a deviation of about half a meter to one meter. You cannot see this from the ground, regardless of how closely you look.
Therefore, anyone looking for eight sides on the Great Pyramid is searching for a feature they cannot visit. You can only photograph it under specific conditions, and that is the real core of this story.
Discovered in 1940, by chance from the air
This was only noticed in 1940, and by chance from the air.
A British pilot photographed the structure during an overflight, and on his image, a faint line appeared on each face running from the base to the apex. It was not a crack or the shadow of a neighboring building, but the ridge between two surfaces with minimally different slopes, made visible by the low sun.
That it took forty-five hundred years for this discovery says less about the attention of earlier observers than about the conditions. The division becomes visible only from the air, only at a specific sun angle, and only as long as the surface is not disturbed by vegetation or weathering shadows. In practice, this means: around the equinoxes, in the morning or evening.
From a surveying perspective, however, the effect has been measurable for a long time. The precise recordings of the structure's geometry work with deviations of this magnitude anyway, because the entire complex is surveyed in arc minutes.
For context, the indentation is primarily documented for the largest structure. The data for the two neighboring pyramids are less clear, partly because their surfaces are preserved differently.
Why the faces are indented
Intention
The indentation was planned, perhaps to stabilize the casing stones or to achieve an optical effect.
Pros
In a structure aligned to within arc minutes, an unintentional deviation of this regularity would be unusual.
Cons
There is no text or evidence proving such an intention, nor any parallel in other pyramids.
Construction method
The layers were placed with a slight inward tilt toward the center, inevitably dimpling the faces.
Pros
An inward-tilted layering increases stability and is documented in other structures.
Cons
It does not explain why the effect occurs so evenly across all four sides.
Settlement
The structure has settled over millennia, causing the surfaces to sink subsequently.
Pros
Settlement in structures of this mass is inevitable.
Cons
Settlement would be uneven, depending on the subsoil. However, the effect is regular.
Loss of casing
The indentation arose only after the smooth outer skin wore away and the core masonry was exposed.
Pros
The core masonry is coarser than the casing and could show this shape.
Cons
Then the effect would occur in all pyramids that have lost their casing, which is not the case.
You will not see it
For your visit, the short answer is: you will not see it. Anyone collecting mathematical facts about the Giza pyramids will find one here that can only be understood through calculation or from the air.
From the ground, a one-degree deviation over 200 meters is imperceptible, especially on a surface of roughly hewn blocks with rubble at the foot. Even standing at a corner doesn't help, because the effect lies in the middle of the face and perspective swallows it up further.
Taking your own aerial photos is also out of the question. Operating drones is generally prohibited in Egypt, and even importing one without permission regularly leads to confiscation. Anyone who wants to see the octagonal nature must rely on existing imagery.
What you can check on site, however, is the precision from which the effect becomes noticeable in the first place. The official description of the structure lists a base side of around 230 meters, and the four sides deviate from each other by only a few centimeters. If you look along a base edge, you see a line that remains straight over this length.
It is precisely for this reason that the octagonal nature is worth reporting. With a poorly constructed structure, a one-degree deviation would have gone unnoticed by everyone.
Frequently asked questions
Does the Great Pyramid have four or eight sides?
Four faces, like every pyramid. Because each face is slightly indented inward, it technically consists of two surfaces, totaling eight.
How strong is the indentation?
Less than one degree. Over a face length of around 200 meters, this corresponds to about half a meter to one meter.
When was this discovered?
In 1940, via an aerial photograph taken when the sun was low. The effect is not perceptible from the ground.
Was the indentation intentional?
Unresolved. Discussed are conscious design, a construction method with inward-tilted layers, settlement, and consequences of the loss of casing.
Can you see it on site?
No. It becomes visible only from the air at the right sun angle, and taking your own aerial photos is not permitted in Egypt.