Sacred Geometries and Their Scientific Meanings

The Interface between Science and the Transcendental

Stephen M. Phillips  


"The Universe is a thought of the Deity. Since this ideal thought-form has overflowed into actuality, and the world born thereof has realized the plan of its creator, it is the calling of all thinking beings to rediscover in this existent whole the original design."

Friedrich Schiller



Inner form of Tree of Life 
How sacred geometries are equivalent to one another, encode the nature of all levels of reality and embody the structure and dynamics of the basic particles of matter.




The 421 polytope has 6720 edges

 The 2-d Sri Yantra has 672 yods other than corners of triangles

The 421 polytope has 6720 edges.

  The Sri Yantra has 672 yods other than corners of triangles.

Weighted with the number 10, the 672 yods other than corners of triangles in the Sri Yantra constructed from tetractyses denote the 6720 edges of the 421 polytope. The 240 corners, sides & triangles surrounding the centre of the Sri Yantra correspond to the 240 vertices of the 421 polytope, which represent the 240 roots of E8, the rank-8, exceptional Lie group associated with E8×E8 heterotic superstring forces. It is implausible to attribute to coincidence both these properties of the Sri Yantra. Rather, they indicate that such superstrings exist and conform to this blueprint as its subatomic realization.

Gosset polytope as inner form of 10 Trees of Life

These analogous features are convincing evidence that the 421 polytope conforms to the archetypal pattern embodied in sacred geometries as it is implausible that they arise by chance. The implication is inescapable: E8×E8 heterotic superstrings exist.

672 yods in 1st 4 Platonic solids

 672 hexagonal yods in 3-torus with Type A triangles

Weighted with the Decad (10), the 672 yods in the first 4 Platonic solids, the faces & interiors of which are constructed from tetractyses, generate the number (6720) of edges of the 421 polytope. 168 yods on average make up these Platonic solids. This shows how these 4 regular polyhedra, thought by the ancient Greeks to be the shapes of the particles of the elements Earth, Water, Air & Fire, embody the basic number (168) characterising the helical form of the E8×E8 heterotic superstring constituents of matter — the "UPAs" remote-viewed by Annie Besant & C.W. Leadbeater 122 years ago. It confirms the ancient intuition that the geometry of the first 4 Platonic solids determines the form of the basic constituents of physical matter.


Weighted with the Decad (10), the 672 hexagonal yods making up the 56 Type A triangles (168 tetractyses) in the {3,7} tessellation on the 3-torus of the 168 automorphisms of the Klein quartic generate the number (6720) of edges of the 421 polytope. The interior angle of the latter's 8 triacontagons formed as Petrie polygons by their 240 vertices is 168°. This association between the numbers 672 & 168 establishes unequivocally the connection between the clairvoyantly obtained structural parameter 168 and the 421 polytope, whose 240 vertices represent the 240 roots of the rank-8 Lie group E8 that appear in E8×E8 heterotic superstring theory.

Proof that the inner form of 10 Trees of Life maps the 421 polytope, whose 240 vertices represent the 240 roots of E8.

The 431 polytope is the inner form of 10 Trees of Life


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Proof that the sacred geometries of religions embody a universal design that encodes the physics of superstrings, the human skeleton, DNA and the mathematics of the seven musical scales.

Extra-sensory Perception
of Quarks
(PDF, 256 pages)

ESP of Quarks


ESP of Quarks & Superstrings
(PDF, 248 pages)

ESP of Quarks & Superstrings

Chapters 1-4   Chapters 5-6

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Outer & inner Tree of Life basis of E8 and E8×E8 (PDF)


Mathematical meanings of the Names of God

Part 1 (PDF)

Part 2 (PDF)

Part 1

Part 2

A short history of the fourth dimension



Part 2

Part 2

The real "God particle"

Re-discovery of the Higgs boson

The sacred geometrical nature of the 421 polytope (PDF)

The Tree of Life basis of the subquark state of the E8×E8 heterotic superstring (PDF)

The UPA & the 421 polytope as the outer & inner forms of 10 Trees of Life (PDF)

How eight sacred geometries embody the 84:84:84:84 division (PDF)

Particle remote-viewed a century ago shown to be an E8×E8 heterotic superstring (PDF)

The inner Tree of Life & the 5 Platonic solids embody the 'fine-structure constant' number 137 (PDF)

The disdyakis triacontahedron embodies the 'fine-structure constant' number 137

The Polyhedral Tree of Life embodies the 'fine-structure constant' number 137

The outer & inner Trees of Life represent the roots of E8 and E8×E8

Sacred-geometrical connections between the UPA and the 421 polytope (PDF)

The outer & inner forms of 10 Trees of Life that map the 10 dimensions of superstring space-time embody the superstring structural parameter 1680 (PDF)

1920 & 3840 embodied in sacred geometries (PDF)