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In his book The Egyptian Pyramids: A Comprehensive, Illustrated Reference, J.P. Lepre wrote:

One very unusual feature of the Great Pyramid is a concavity of the core that makes the monument an eight-sided figure, rather than four-sided like every other Egyptian pyramid. That is to say, that its four sides are hollowed in or indented along their central lines, from base to peak. This concavity divides each of the apparent four sides in half, creating a very special and unusual eight-sided pyramid; and it is executed to such an extraordinary degree of precision as to enter the realm of the uncanny. For, viewed from any ground position or distance, this concavity is quite invisible to the naked eye. The hollowing-in can be noticed only from the air, and only at certain times of the day. This explains why virtually every available photograph of the Great Pyramid does not show the hollowing-in phenomenon, and why the concavity was never discovered until the age of aviation. It was discovered quite by accident in 1940, when a British Air Force pilot, P. Groves, was flying over the pyramid. He happened to notice the concavity and captured it in the now-famous photograph. [p. 65]
This strange feature was not first observed in 1940. It was illustrated in La Description de l'Egypte in the late 1700's (Volume V, pl. 8). Flinders Petrie noticed a hollowing in the core masonry in the center of each face and wrote that he "continually observed that the courses of the core had dips of as much as ½° to 1°" (The Pyramids and Temples of Gizeh, 1883, p. 421). Though it is apparently more easily observed from the air, the concavity is measurable and is visible from the ground under favorable lighting conditions.

I.E.S. Edwards wrote, "In the Great Pyramid the packing-blocks were laid in such a way that they sloped slightly inwards towards the centre of each course, with a result that a noticeable depression runs down the middle of each face -- a peculiarity shared, as far as is known, by no other pyramid" (The Pyramids of Egypt, 1975, p. 207). Maragioglio and Rinaldi described a similar concavity on the pyramid of Menkaure, the third pyramid at Giza. Miroslav Verner wrote that the faces of the Red Pyramid at Dahshur are also "slightly concave."

What was the purpose for concave Great Pyramid sides? Maragioglio and Rinaldi felt this feature would help bond the casing to the core. Verner agreed: "As in the case of the earlier Red Pyramid, the slightly concave walls were intended to increase the stability of the pyramid's mantle [i.e. casing stones]" (The Pyramids, 2001, p. 195). Martin Isler outlined the various theories in his article "Concerning the Concave Faces on the Great Pyramid" (Journal of the American Research Center in Egypt, 20:1983, pp. 27-32):

To give a curved form to the nucleus in order to prevent the faces from sliding.
The casing block in the center would be larger and would serve more suitably as a guide for other blocks in the same course.
To better bond the nucleus to the casing.
For aesthetic reasons, as concave faces would make the structure more pleasing to the eye.
When the casing stones were later removed, they were tumbled down the faces, and thereby wore down the center of the pyramids more than the edges.
Natural erosion of wind-swept sand had a greater effect on the center.
Isler dismisses the first four reasons based on the idea that "what is proposed for the first pyramid should hold true for the others." He also dismisses the last two because they would not "dip the courses," but rather have simply "worn away the surface of the stone." Adding another category to the list above, "a result of imperfect building method," he proceeds to theorize that the concavity was an artifact of a compounding error in building technique (specifically, a sag in the mason's line). One is tempted to reject this theory based on Isler's own reasoning: "what is proposed for the first pyramid should hold true for the others."

The concavity has prompted more improbable theories, usually in support of some larger agenda. David Davidson (cited by Peter Tompkins in Secrets of the Great Pyramid, pp. 108-114) defended the discredited Piazzi Smyth by attempting to demonstrate that if measurements included the hollowing, they would provide three base measurements that describe the three lengths of the year: solar, sidereal, and "anomalistic." (These lines, on the diagram below, would be AB, AEFB, and AMB.) What Davidson is assuming is that the concavity, present today in the core structure of the pyramid, would extend to the finished cased surface. There is no evidence for this; indeed the extant casing is perfectly flat. Maragioglio and Rinaldi observed that the granite casing of Menkaure's pyramid was flat, but above the granite the packing-blocks formed a concavity in the center of each face. The evidence indicates that the concavity is a functional feature of the core structure that was hidden from sight when the casing stones were applied.