The profile of Khafre exemplifies the 345 triangle – the pyramid profile is contained within a 3 X 2 rectangle; or the figure of the vesica piscis. The height of the pyramid is 274 and the base is 411 cubits. 411 =3 x 137. Lehner has estimated the original base of Sphinx (before the stone cladding and later repairs) as 137 cubits. It is important to note that the Sphinx was excavated from the rock to provide blocks for the adjacent Sphinx temple (as the tracing of the same geological structure common to both proves) which rather contradicts claims for extreme antiquity.
The passage system of Khafre is shown below –
– notice the 2 cubit thick granite casing course at the bottom.
The meridian section of the pyramid is a 345 triangle. This is apparently echoed in the mortuary temple –
The width of this temple is 88 cubits (drawn on the right) –
– the pyramid on the left is Khufu. Figures are only certain for the eastern part of the peribolus walls. It is interesting to note the repeated use of the factors 7, 11, and 17.
Petrie did not survey the interiors of Khafre and Menkaure, mostly confining himself to comments on chamber dimensioning. In the 1960’s Maragoglio and Rinaldi published a survey of Giza and this source is usually cited by scholars for interior measurements, in this case Khafre.
Within the pyramid there two passage angles – the upper passage laid out on the diagonal of the double square (in red), and the lower passage laid out on the diagonal of a 2 X 5 rectangle (in blue) –
– the profile of the pyramid is height 274, base 205.5 (or SEKED 5 palms 1 finger) and slope 342.5 cubits.
The figure below appears to define the height of the entrance above base, but there is a small conflict with Maragioglio and Rinaldi’s figures –
Legon decided to take his own measurements, and by so doing discovered a very elegant design, laid out in palms and digits –
It would seem from this that the basic plan has been very subtly modified. Here the two schemes are compared –
– the red diagonal from A intersects the casing at B. The red line C-D intersects the diagonal of the double square at E. Legon’s analysis is overlaid in blue.
Many years ago Khafre was scanned using high tech methods but no upper chambers were detected – the pyramid appears to be a solid mass and it is difficult to understand why such an imposing structure, occupying the most favoured position on the plateau, has a relatively simple passage system bearing no relation to the kind of geometry found inside Khufu. Legon concluded that the plan for the passages, rather than being derived from the profile of the pyramid is a model of the north/south distance between the north bases of Khufu and Khafre (440 + 250 = 690) –
(It is incidentally worth noting that the horizontal distance between the sarcophagus chamber and lower chamber in Khafre (146 cubits) is approximately equal to the distance between Khufu centre and passage junction.)
The pyramid of Khafre then appears as something of an ‘adjunct’ to Khufu. Indeed a number of scholars have suggested that because the orientations of Khufu and Khafre are so similar the two pyramids were laid out together.
When Legon began his analysis of the Giza plateau, he noticed that the south base of Khafre is 5 half bases (1100 cubits) south of Khufu north base –
– he also saw that Khufu and Khafre are separated by a rectangle approximately measuring 250 by 625 cubits. This was the preliminary plan – one cubit was subtracted from the west and added to the south, making a rectangle of dimensions east/west 1064 and north/south 1101.
It is therefore interesting to note that the base of Khafre, if ‘extended’ fivefold in the manner of Khufu (but inverted south to north), locates the passage junction in Khufu –
This arrangement emphasizes the theme of 2 X 5, also found in the plan of Khafre’s sarcophagus (below), the lower passage angle, and curiously the plan of Menkaure sarcophagus chamber –