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ULTIMATE SYMMETRY:

Fractal Complex-Time and Quantum Gravity

by Mohamed Haj Yousef



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IV.3.3 The Octahedron


The Octahedron has eight triangular faces, six vertices, and twelve edges. A regular Octahedron consists of eight equilateral triangles, with four of those triangles meeting at each vertex. It is in fact the only one of the regular polyhedra to have an even number of faces meeting at a single vertex. Various minerals have been found in the form of octahedral crystals, including diamond, alum and fluorite. Interestingly, there are two different vertex angles: at any vertex, the angle between adjacent edges is sixty degrees, whereas the angle between opposite edges is ninety degrees.

Figure IV.6: The Octahedron, eight triangular faces, six vertices, and twelve edges, and its the dual of the Hexahedron.

As we mentioned above, Plato suggested that the Octahedron corresponds to the element Air, since its minuscule components are so smooth that one can barely feel it. This goes well in accordance with the complex-geometry of time as we noted above, since the Octahedron is the dual of Hexahedron and they both form two mutually orthogonal arrows of time which are the folds of super-symmetry, as we explained in Chapter II.

 



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  • ... that one can barely feel it. This goes well in accordance with the complex-geometry of time as we noted above, since the Octahedron is the dual of Hexahedron and they both form two mutually ORTHOGONAL ARROW s of time which are the folds of super-symmetry, as we explained in Chapter II. &nbs ...


  • ... Regular Polyhedra =>:

  • ... r faces, six vertices, and twelve edges. A regular Octahedron consists of eight equilateral triangles, with four of those triangles meeting at each vertex. It is in fact the only one of the REGULAR POLYHEDRA to have an even number of faces meeting at a single vertex. Various minerals have ...


  • ... Orthogonal Arrows =>:

  • ... that one can barely feel it. This goes well in accordance with the complex-geometry of time as we noted above, since the Octahedron is the dual of Hexahedron and they both form two mutually ORTHOGONAL ARROWS of time which are the folds of super-symmetry, as we explained in Chapter II. &nbs ...


  • ... Equilateral Triangle =>:

  • ... Gravity by Mohamed Haj Yousef Search Inside this Book IV.3.3 The Octahedron The Octahedron has eight triangular faces, six vertices, and twelve edges. A regular Octahedron consists of eight EQUILATERAL TRIANGLE s, with four of those triangles meeting at each vertex. It is in fact the only o ...


  • ... Adjacent Edges =>:

  • ... ous minerals have been found in the form of octahedral crystals, including diamond, alum and fluorite. Interestingly, there are two different vertex angles: at any vertex, the angle between ADJACENT EDGES is sixty degrees, whereas the angle between opposite edges is ninety degrees. Figure ...


  • ... Triangles Meeting =>:

  • ... e this Book IV.3.3 The Octahedron The Octahedron has eight triangular faces, six vertices, and twelve edges. A regular Octahedron consists of eight equilateral triangles, with four of those TRIANGLES MEETING at each vertex. It is in fact the only one of the regular polyhedra to have an eve ...


  • ... Mutually Orthogonal =>:

  • ... o smooth that one can barely feel it. This goes well in accordance with the complex-geometry of time as we noted above, since the Octahedron is the dual of Hexahedron and they both form two MUTUALLY ORTHOGONAL arrows of time which are the folds of super-symmetry, as we explained in Chapter ...


  • ... Barely Feel =>:

  • ... ges, and its the dual of the Hexahedron. As we mentioned above, Plato suggested that the Octahedron corresponds to the element Air, since its minuscule components are so smooth that one can BARELY FEEL it. This goes well in accordance with the complex-geometry of time as we noted above, si ...


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Message from the Author:

I have no doubt that this is the most significant discovery in the history of mathematics, physics and philosophy, ever!

By revealing the mystery of the connection between discreteness and contintuity, this novel understanding of the complex (time-time) geometry, will cause a paradigm shift in our knowledge of the fundamental nature of the cosmos and its corporeal and incorporeal structures.

Enjoy reading...

Mohamed Haj Yousef


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