Mandalic geometry and polar coordinates - IV
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LEVELS 1 and 5
9-Six hexagrams reside at Level 1 and six at Level 5. These occur in groups of two at each of three points in Level 1 and in groups of two at each of three points in Level 5. The hexagrams in Level 1 all contain a single positive (yang) line and the hexagrams in Level 5 all contain a single negative (yin) line. In both Level 1 and Level 5 the three resident groups are situated 120° from one another. The three groups of Level 5, however, are phased 60° from those of Level 1. All these points and hexagrams are found in Shell 2 of the spherical mandala. In the Cartesian form of the mandala these points and hexagrams are the cube edge centers closest to the maximum yin and maximum yang hexagrams or vertices. There are six other points, each with two resident hexagrams, in Shell 2 but these will all soon be seen to lie at Level 3.
10-Connecting the points of the three groups in Level 1 or Level 5 results in an equilateral triangle. If one were to look down (or up) at these two triangles superimposed upon one another one would see a 6-pointed star. This of course hearkens back to a lot of intellectual history through the ages having historical, religious and cultural contexts. The 6-pointed star, for example, has significance to sacred geometry as it is the compound of two equilateral triangles, the intersection of which is a regular hexagon.
Of particular note here, however, is the fact that in mathematics, the root system for the simple Lie group G2 is in the form of a hexagram [6-pointed star].
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© 2013 Martin Hauser