In the image on the left above, the right axes are horizontal and the diagonals are on sixty degrees, forming 'upright' equilateral triangles. In this view we see a hexagon composed of six triangles.

Here we see that another way to generate the equilateral triangle, rhombus, hexagon, cube, etc is with the vesica piscis. The side of the blue triangle is equal to the diameter of the circles. The short axis of the rhombus is equal to the radius. A line from a corner to the mid-point of the opposite side bisects that angle. If the radius of the circles (the short axis of the rhombus) is 1 then the long axis is 1.732 (sqrt of 3).

Starting with the Vesica-pisces...from which one is able to produce...

Sacred Geometry and the Great Pyramid of Giza:   The exterior angle of the 'Great pyramid of Giza' can be reproduced with the Vesica-pisces. It has been long suspected that the Great pyramid was a subsidiary of geometric knowledge. There are several other indications that sacred geometry was an important factor in the design of the pyramid. The Sacred mean (Phi), was also recorded into the dimensions of the pyramid itself.   Pi and the Pyramid. Egyptian mathematicians arrived at a figure of 3.16 (as shown on the Rhind Papyrus), written 600 to 800 years later and far cruder than the precise ratio the great Pyramid seems to express. The figure of Pi is recorded into the dimensions of the Great Pyramid several  times; As well as the Height/Perimeter ratio of the pyramid itself (2 ∏x H = Perimeter) The perimeter of its main compartment, the so called “King’s Chamber,” is also exactly 3.14 times its length, and the large granite coffer or sarcophagus in this room shows the same proportion. In the earlier, rhomboidal or “Bent Pyramid” at Dashur, a few miles to the south, the sides begin to ascend at the same 2-Pi angle as the Great Pyramid, then change half way up to 3-Pi (43 ½º ) ratio. (More on the Geometry of the Great pyramid)     Pyramid Geometry and Latitude. The exterior angle of the Great pyramid is the exact same latitude that Silbury Hill was built, and at the same time. It is perhaps no coincidence to find that exterior angle of the Silbury monument has an exterior angle of 30 °, the same as the latitude of Giza.  This exact angle is also found at nearby Stonehenge in the orientation of The Avenue, which points towards the sunrise on the summer solstice. Stonehenge sits exactly 1/4 of a degree of longitude south of Avebury. This fact is just one of many in the increasingly convincing argument in favour of the existence of applied sacred geometry in prehistory. (British Geodesy)      (Egyptian Geodesy) (Geodesy Homepage)

An Equilateral triangle, Hexagon, Pentagon, Square and so on and so on..