Mandalic geometry and polar coordinates - VIII
(Continued from here.)
LEVEL 3 (cont.)
12-Subgroups of Level 3 (cont.)
B-Concluding our survey of the spherical mandala we come to the second subgroup of hexagrams of Level 3, the level of charge density neutrality. These 12 hexagrams in groupings of two occupy six points in Shell 2 (heading from outer to inner) as do (together) the hexagrams in Levels 1 and 5 which have one solid (yang) line and 5 solid (yang) lines respectively. Along with the 8 hexagrams of subgroup A found in Shell 4 at the center of the spherical mandala these 12 hexagrams form the entire Level 3. Unlike those eight hexagrams discussed in the previous post, these twelve are each constructed from two trigrams which are not complements of one another while still retaining charge density neutrality. In some ways these six groups are the most mysterious of all the hexagram groups.
So to clarify, we are talking here about six equidistant points about the equatorial great circle of Shell 2 (from outer to inner) of the spherical mandala. That means the six groups are separated one from the next by 60°. We can anticipate that these consist of two sub-subgroups of points and hexagrams separated by 120° forming two equilateral triangles which are out of phase by 60°, creating still another 6-pointed star. Mathematics is so remarkably consistent. More to the point though, - - - because (and we are getting ahead of ourselves here) we are talking (or will be at some future time) not just about geometric points but about particles, force fields and strings as well - - - all these triangles, angles and 6-pointed stars give rise to various symmetries which in turn give rise to physics as it is.
LEVEL 3, GROUP B HEXAGRAMS
Of particular note here is the fact that the two hexagrams in row 1 and the two in row 4 above are unique in that the inverse of each of these hexagrams is identical to its complement. That means in some sense the anti-hexagram for each of these hexagrams dwells close within. There are only four other hexagrams out of the 64 that share this property. Those four also reside at Level 3 of the spherical mandala but are among the eight at the center point (Shell 4) in Group A. This attribute will come into play again in future posts when we address the subject of hexagrams as particle analogues and intersecting strings.
© 2013 Martin Hauser