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## The hexagonal rod rotation 2

Returning to the hexagonal rod, the interactive drawing shows the dynamic system of geometry that forms that rod and which was explained on the earlier page (page C10), and the clock has been automatically started. Zoom in on the area where the intersect point of the ascending passage line and the lower northern shaft is plotting out the upright hexagonal rod.

Starting with this plot there are three operation that need to be applied to the geometric plot of the rod.

### The first - rotation

The first step, logically, is to rotate the hexagonal rod in 3D by 40°, which is the approximate angle of the lower northern shaft, so that the rod fits in to the shaft properly. Click here to display the dynamic intersect point rotated into the shaft. Allow the interactive drawing time to plot out the rotated rod clearly and you can see that the original upright plot of the rod has now been angled by 40° into the screen on the second plot line.

It is important to keep track of the two plots. The longer plot is the original perfect mathematics plot of the rod and the shorter plot is the rotated rod which is formed from an approximate shaft angle and is therefore defined only to the precision of the surveying measurement of the shaft.

### The second - rotations

The second rotation, which comes from understanding that in the architecture up to this point every time something has been created then the opposite has also been created, is to reverse the two plots. Click here to add 180° to the rotation angles and reverse them.

### The third - reflection

The third operation, which is implied by the double black line on the wall, is to reflect the longer of the two plot lines in a vertical axis. Click here to reflect this plot point in a vertical axis which passes through the upper end of the straight section of the rod.

### The key

Allow the plot to develop and then overlay a picture of the 'hook' that was found in the shaft onto the drawing.

The 'hook' is actually the key to the pyramid. As can be seen on the drawing, when the geometric system upon which the pyramid's architecture is based is correctly re-created it matches the shape of the key, which is a metal casting of the mathematical plot of the ascending passage and lower northern shaft's intersect point in the dynamic geometry.

The geometric plot is remarkable, but does contain some small discrepancies from the exact shape and size of the 'hook' which are rectified later in this work. What is most important from the logic perspective is to understand that the left arm of the key is mathematically perfect, and the right arm contains the surveying errors of the shaft's angle, which are substantial.

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Last edited: 3rd July 2019
Last code/graphics edit: 29th March 2021