Front page > Geometry based on Silver Ratio and Golden Ratio > Sacred Geometry: Cuboctahedron and Tetrahedron are both based on the Silver Ratio.

Released on Nov. 11, 2011, the movie titled “Thrive” aims at having all the mankind equally thrive. Anyone, irrespective of age and sex, cannot but feel that argument and issues raised by this movie are significantly related to all aspects of everyday life. It makes a great impact on our perception and awareness. I understand that more than 4 million people have already seen the movie, which is now free to watch online in 17 languages (with more coming soon) at www.thrivemovement.com/the_movie. This movie gives clear and detailed explanations on: (1) fundamental structure of the universe, (2) real existence of technologies to get out free energy that is derived from it, (3) dream world realized by its practical application, (4) existence of extraterrestrial intelligence engaged on with good will and unconditional love, (5) true monarch’s cruel plan for population cutback and exhaustive domination that is the current underlying problem of the world, (6) controversial points concerning the right to print paper money that is the source of such power, and so forth. It is actually bringing things out so that everybody can understand. Of these crucial issues, the first one is in the category of sacred geometry and, therefore, I will put a focus on it here in this article.

This movie was produced and hosted by Mr. Foster Gamble who is a scientist. Having been engaged in research activities for many decades, Mr. Gamble was convinced, according to his account, that the torus forms the basis of all the mechanism of the universe. (Reference: In geometry, a torus is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a ring torus or simply torus if the ring shape is implicit.)

Mr. Gamble also states that the energy in the torus flows in through one end, circulates around the center and exits out the other side. It is balanced, self-regulating and always whole. He further states as follows. The torus is like the breath of the universe. It is the form the flow of energy takes at every scale of existence. But it also serves as the underlying structure like a skeleton making the flow fit together. It is called the vector equilibrium that is a term coined by one of Twentieth Century’s greatest thinkers, Mr. Buckminster Fuller. This solid is the same as cuboctahedron. Inspired by Fuller’s visionary work, Mr. Gamble did research on the vector equilibrium and the torus for scores of years and, as a result, he was convinced that the torus and the vector equilibrium are the basic patterns, fundamental to the creation of the universe at all scales.

Mr. Nassim Haramein is a cosmologist, pioneering physicist and inventor. During the interview by Mr. Gamble, he referred to the flower of life discovered

in the Osirian Temple in Abydos, Egypt. This figure has also been found in a variety of ancient literatures and remains since time began. According to Mr. Haramein, this graphic is elicited from a matrix where 64 tetrahedra (i.e. triangular pyramids) can be arranged in the vector equilibrium and it represents 64 different energy units. He continued to mention that the torus and vector equilibrium (i.e. cuboctahedron), particularly the crystallization of 64 tetrahedra, show us how the energy of the universe functions and that they encourage us in harmonizing with it.

The most significant point in this regard is that the aforementioned two kinds of solid, i.e. cuboctahedron and tetrahedron, are both based on the Silver Ratio. This fact is also mentioned in my mathematical paper uploaded in this website. Please refer to “Complementary Relationship between the Golden Ratio and the Silver Ratio in the Three-Dimensional Space & “Golden Transformation” and “Silver Transformation” applied to Duals of Semi-regular Convex Polyhedra“. The following are excerpts from it relevant to this point.

**Cuboctahedron**: ”The cuboctahedron is made by connecting the middle point of each edge of either the cube or the regular octahedron. These solids are both based on the Silver Ratio.

**Regulatr tetrahedron**: The dihedral angle is 70°31’43”. This is the same as the acute angle of the silver rhombus with a ratio of the short diagonal to the long diagonal being equal to the Silver Ratio. The obtuse angle of the isosceles triangle made by connecting the center of the gravity with any two vertices is 109°28’. This is the same as the obtuse angle of the silver rhombus.

The foregoing seems to indicate that it is not the Golden Ratio but the Silver Ratio that constitutes the bedrock of the creation of the universe at all scales. This is interesting.

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Thank you for your nice comment. I am currently at the last stage of preparing a mathematical paper. It is to be contributed to a leading American mathematical journal. As soon as it is successfully placed in it, I willl upload it in my website along with other articles in the same field. You can surely count on them.

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Thank you for your comment. The article in question was a product of my study a couple of years ago. A good progress has been made in it quite recently. I plan to sum up my findings in a paper and contribute it to a leading U.S. mathematical journal shorly. As soon as it is successfully placed in that journal, I will upload it in my website.

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