In this section, various sacred geometries are shown to have analogous, mathematical properties. This indicates that they are equivalent as maps of physical and superphysical levels of reality, as illustrated in the section Maps of reality.
In the section Superstrings as sacred geometry, these sacred geometries are proved to embody the basic structural and dynamical parameters of the E8×E8 heterotic superstring and to confirm the paranormal observations of this fundamental subatomic particle published in 1908 by the Theosophists Annie Besant and C.W. Leadbeater in their book Occult Chemistry, as discussed in the section Occult Chemistry and as analysed in the section Remote viewing of atoms.
In the section 4-d sacred geometries, the yod and geometrical compositions of the 4-dimensional regular polytopes called the "polychorons" are analysed. The sacred-geometrical basis of the 421 polytope, known to represent the 240 roots of E8, is established.
In the section The seven musical scales, the sacred geometries are shown to be geometrical representations of the intervals between the notes of the seven musical scales, which became the musical modes for the plainsong used for hundreds of years in the liturgies of the Roman Catholic Church.
In the section Plato's Lambda, various sacred geometries are proved to embody certain proportions of a tetractys of numbers extrapolated from the set of numbers which generated the mathematical harmonies of the celestial sphere, according to Plato. Generalisation of this array of numbers reveals its full, archetypal meaning and connection to these sacred geometries.
In the section Human skeleton, the bone composition of the human skeleton is derived in terms of the inner form of its Tree of Life representation.
In the section Wonders of sacred geometry, examples of sacred geometries are discussed that provide especially compelling evidence for the transcendental intelligence that is their ultimate source.
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