|A synopsis of the view of how the pyramid or triangle shape of flames, which "like a pyramid" as Theophrastus says, and Democritus attempts to explain, some arguing that the fire element or atom of fire (fire atom) was a "pyramid" in shape and or sphere (Aristotle, c.350BC) or "tetrahedron" in shape (Plato, c.360BC), derived from Egypt, as espoused in the Heliopolis creation myth, and the sun or sun god being born out of the tip of the great pyramids in the form of the phoenix or benben bird, a geometry learned by the Greeks who travelled there to study, modifying it accordingly.|
In c.2600BC, Imhotep built the step pyramid, a “pyramid” shaped tomb of sorts for the pharaohs, out of the tip of which the sun god, e.g. Ra, was said to be reborn. The precursor the step pyramids, in turn, were “cube” or “rectangle” shaped mastabas (Ѻ), or burial tombs, which over time began to be stacked on top of each other.
In 600-300BC, the Greek scholars all travelled to Egypt to learn their sciences, e.g. geometry, astronomy, and theology.
In 420BC, Democritus, in particular, travelled there, supposedly coming away with the puzzle as to why fires are “pyramid shaped” and the model that fire atoms are either pyramid shaped, like the Egyptian pyramids or spherical, like the sun.
In 360BC, Plato, in his Timaeus, influenced the previous Greek thinkers, outlined his so-called Platonic solid (Ѻ) model of the elements, where earth was a cube, possibly like the mastaba shape, and fire was a tetrahedron, like the pyramid shape.
In the millennia to follow, the pyramid became symbolized by the triangle shape or Greek delta Δ symbol, representative of heat or fire.
The following are related quotes:
“Though it was primarily with reference to the properties and powers and motions of bodies that they assigned them their shapes, the latter are inappropriate. For instance, since fire is mobile, and since it heats and burns some made it a sphere, others a pyramid. They are the most mobile since they are in contact with the fewest things and have the smallest base, the most productive of heat and burning because the one, the sphere, is an angle all over, while the other, the pyramid, has the sharpest angles, and heat and burning are produced by the angles, so they say. Next, if what is burned is set on fire, and fire is a sphere or a pyramid, what is burned has to become spheres or pyramids.”— Aristotle (c.350BC), De Caelo (306a26-307b5) 
“There is also the problem of why a flame is shaped like a pyramid. Democritus says that as its extremities cool down it contracts into a small shape and eventually tapers to a point.”— Theophrastus (c.320BC), On Fire (52) 
“And if the inscription on the ancient pyramid of Sais says, ‘I am all that is, that was, and that will be, no mortal man has yet removed the veil’, it might be replied thereto, that modern science has removed the veil and has discovered that force and matter were, are, and will be.”— Franz Pisko (c.1875), front matter quotes to Ludwig Buchner’s Force and Matter 
“Religion is 70 percent mythology (i.e. Anunian theology), 15 percent astronomy (Sirius = Sarah), 7 percent geology (Nun = annual Nile flood), 5 percent natural science (e.g. dung beetles mounds = pyramids), and 3 percent pixie dust (i.e. fairy tale).”— Libb Thims (2015), reflection on George Millin's 1896 attempt to relegate all religion to myth and good and evil to physical science, 12:14 PM CST Dec 15
1. Taylor, C.C.W. (1999). The Atomists: Leucippus and Democritus: Fragments: a Text and Translation with a Commentary by C.C.W. Taylor (pyramid, pgs. 85-86; 133). University of Toronto Press.
2. Buchner, Ludwig. (1855). Force and Matter: Principles of the Natural Order of the Universe, with a System of Morality Based Thereon (15th German edition; 4th English edition) (pg. 1). London: Asher and Co, 1884.
● Pyramid – Wikipedia.