4dimensional 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 4_{21} polytope representing the 240 roots of E_{8}. 
#3  The sacredgeometrical basis of the five revolutions of each whorl of the UPA/E_{8}×E_{8} heterotic superstring. 
#4  The sacredgeometrical character of the 24cell. 
#5  A 2ndorder tetractys representation of the compound of two 600cells. 
#6  A 3rdorder tetractys representation of the compound of two 600cells. 
The Pythagorean musical counterpart of the disdyakis triacontahedron & the compound of two 600cells determining E_{8}.  
#8  The correspondence between the 24cell and the 3dimensional Sri Yantra. 
#9  The correspondence between the 24cell and the two Type B dodecagons. 
#10  The correspondence between the 24cell and the seven separate Type B polygons. 
#11  The 4_{21} polytope as the inner form of 10 Trees of Life. 
#12  Arithmetic connections between the 4_{21} polytope and the Tree of Life. 
#13  Square representations of some parameters of the 4_{21} polytope. 
#14  Pentagramic representation of the geometrical composition of the 4_{21} polytope. 
#15  The first four Platonic solids embody the number of edges of the 4_{21} polytope. 
#16  The 2d Sri Yantra embodies the number of edges of the 4_{21} polytope. 
#17  The pair of Type C dodecagons embodies the number of edges of the 4_{21} polytope. 
#18  The disdyakis triacontahedron embodies the number of edges of the 4_{21} polytope. 
#19  The Godname EL CHAI prescribes the number of edges of the 4_{21} polytope. 
#20  The 24cell embodies the holistic parameter 672. 
#21 
The 4_{21} 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 & 3polytopes in the 24cell. 
#23  How the Kabbalistic Godnames prescribe the 4_{21} polytope. 
#24  The 4_{21} polytope as the inner form of 10 Trees of Life. 
The triacontagon
#1 
The eight triacontagons in the E_{8} Coxeter plane projection of the 4_{21} 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 4_{21} polytope and each half of the inner form of 10 Trees of Life. 

#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 E_{8} Coxeter plane projection of the 4_{21} polytope. 