Certainly the shape of the first dome must be semispherical or at least that of a section of a sphere, in order to account for the rotation of the planets/stars.
Could the FE shape be a square? Then, we must rotate that square by an angle of 23.5 degrees (in order to account for the orbit of the Sun). And have a section of a sphere placed upon it.
The time of the summer and winter solstice is marked by straight lines of 28 degrees each drawn from the apex of Khefren.
The summer solstice is marked by a straight line starting at the pyramid’s apex and going 28 degrees North (from West to East direction) placed on the drawing by J.A.R. Legon in 2000 (27.95 degrees). The line of the winter solstice can be determined by mirroring that line in Southern direction. The north-eastern foot-point of the limestone Khentkawes will be the location of the winter solstice. As the years can be divided into two equal parts this way, the division of the year into two parts was created. The summer solstice is connected to the 21st of June, while the winter solstice to the 21st of December. Today, there are 6 months between the two dates.
Then, given the 1.5 km westward precessional shift of the Sun, and using a distance of 6,363.63 km from the center of the square to one of its sides, the length of the entire history would amount to 375 years (with a circle and the same radius, the length is 339 years).
It all comes down to this: does the Sun's precessional shift take place on an arc of a circle, or on a side of a square?