4-dimensional Sacred Geometries
(Click on the page numbers)
The Polychorons & the Gosset Polytope
| #1 |
The 6 polychorons. |
| #2 |
The 10×24 division in sacred geometries & its realisation in the 421 polytope representing the 240 roots of E8. |
| #3 | The sacred-geometrical basis of the five revolutions of each whorl of the UPA/E8×E8 heterotic superstring. |
| #4 | The sacred-geometrical character of the 24-cell. |
| #5 | A 2nd-order tetractys representation of the compound of two 600-cells. |
| #6 | A 3rd-order tetractys representation of the compound of two 600-cells. |
| The Pythagorean musical counterpart of the disdyakis triacontahedron & the compound of two 600-cells determining E8. | |
| #8 | The correspondence between the 24-cell and the 3-dimensional Sri Yantra. |
| #9 | The correspondence between the 24-cell and the two Type B dodecagons. |
| #10 | The correspondence between the 24-cell and the seven separate Type B polygons. |
| #11 | The 421 polytope as the inner form of 10 Trees of Life. |
| #12 | Arithmetic connections between the 421 polytope and the Tree of Life. |
| #13 | Square representations of some parameters of the 421 polytope. |
| #14 | Pentagramic representation of the geometrical composition of the 421 polytope. |
| #15 | The first four Platonic solids embody the number of edges of the 421 polytope. |
| #16 | The 2-d Sri Yantra embodies the number of edges of the 421 polytope. |
| #17 | The pair of Type C dodecagons embodies the number of edges of the 421 polytope. |
| #18 | The disdyakis triacontahedron embodies the number of edges of the 421 polytope. |
| #19 | The Godname EL CHAI prescribes the number of edges of the 421 polytope. |
| #20 | The 24-cell embodies the holistic parameter 672. |
| #21 |
The 421 polytope as the inner form of the Tree of Life. |
| #22 | How the Type B square and octagon embody the numbers of 0-, 1-, 2- & 3-polytopes in the 24-cell. |
| #23 | How the Kabbalistic Godnames prescribe the 421 polytope. |
| #24 | The 421 polytope as the inner form of 10 Trees of Life. |
The triacontagon
| #1 |
The eight triacontagons in the E8 Coxeter plane projection of the 421 polytope. |
| #2 |
The Lambda Tetractys pattern of the interior & vertex angles of the triacontagon. |
| #3 |
The sum of the interior angles of the 8 triacontagons is the yod population if the inner form of 10 Trees of Life with Type C polygons. |
| #4 |
The triacontagon has the holistic pattern of the Type B dodecagon & the disdyakis triacontahedron. |
| #5 |
The pattern of interior & vertex angles in 8 sectors of the 8 triacontagons matches the yod population of the (7+7) Type B polygons. |
| #6 |
The yod population of the (4+4) Type A triacontagons matches that of the (7+7) Type B polygons. |
|
A correspondence between the 421 polytope and each half of the inner form of 10 Trees of Life. |
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| #8 |
The yods in the (4+4) triacontagons denote the turns in one revolution of the 10 helical whorls of the UPA. |
| #9 |
The inner form of 10 Trees of Life embodies the number of geometrical elements in the 8 Type C triacontagons. |
| #10 |
How 8 sacred geometries embody the 84:84:84:84 pattern of base angles in the triacontagon. |
| #11 |
Interior & vertex angles of the triacontagon conform to the I Ching pattern of 64 hexagrams. |
| #12 |
The yod population of the 8 Type B triacontagons is the structural parameter of the UPA. |
| #13 |
The geometrical composition of the 8 triacontagons. |
| #14 | The dodecagons in the inner form of 10 Trees of Life embody the 16800 turns in the 10 helical whorls of the UPA. |
| #15 | The 8 triacontagons embody the global structural parameter of the UPA. |
| #16 | The (4+4)×30 pattern of the 8 triacontagons in some sacred geometries. |
| #17 |
The 8 Church modes as the musical counterpart of the pattern of 8 triacontagons in the E8 Coxeter plane projection of the 421 polytope. |
