The 10-fold UPA/superstring as the 10-fold division in the
geometrical composition of the pair of Type A dodecagons
As 168 yods are needed to construct the Type A dodecagon from tetractyses,
i.e., it embodies the number that determines the structure of the UPA/heterotic superstring, it should come as
no surprise that its geometry also embodies the 10-fold pattern of this particle, as now proved.
The pair of Type A dodecagons has 24 corners, 24 red sides & 24 blue, radial sides, i.e.,
three sets of 24 geometrical elements. Each sector is divided into three triangles with three green sides and
one internal corner, apart from the shared centre of the dodecagon. Hence, the 24 sectors are, additionally,
composed of 24 internal corners, three sets of 24 green sides and three sets of 24 triangles, i.e., seven sets
of 24 geometrical elements. The pair of Type A dodecagons therefore naturally comprises ten sets
of 24 geometrical elements. These sets are the counterpart of the ten whorls of the UPA/heterotic superstring,
each of which carries 24 gauge charges of the superstring gauge symmetry group E8. The three sets
of 24 corners & sides that create the 24 sectors of the two dodecagons correspond to the three major
whorls of the UPA, each carrying 24 E8 gauge charges. The seven extra sets of 24 elements
needed to turn the dodecagon into a Type A dodecagon correspond to the seven minor whorls, each carrying 24
E8 gauge charges. We saw previously that the 120 yods lining the 42 sides of the seven
enfolded polygons divide into ten sets of 12, further divided into three sets (corners) and seven sets
(hexagonal yods). Each yod symbolizes one of the geometrical elements making up the Type A dodecagon.
The pair of Type A dodecagons has 24 corners, 24 red sides & 24 blue, radial sides, i.e.,
three sets of 24 geometrical elements. Each sector is divided into three triangles with three green sides and
one internal corner, apart from the shared centre of the dodecagon. Hence, the 24 sectors are, additionally,
composed of 24 internal corners, three sets of 24 green sides and three sets of 24 triangles, i.e., seven sets
of 24 geometrical elements. The pair of Type A dodecagons therefore naturally comprises ten sets
of 24 geometrical elements. These sets are the counterpart of the ten whorls of the UPA/heterotic superstring,
each of which carries 24 gauge charges of the superstring gauge symmetry group E8. The three sets
of 24 corners & sides that create the 24 sectors of the two dodecagons correspond to the three major
whorls of the UPA, each carrying 24 E8 gauge charges. The seven extra sets of 24 elements
needed to turn the dodecagon into a Type A dodecagon correspond to the seven minor whorls, each carrying 24
E8 gauge charges. We saw previously that the 120 yods lining the 42 sides of the seven
enfolded polygons divide into ten sets of 12, further divided into three sets (corners) and seven sets
(hexagonal yods). Each yod symbolizes one of the geometrical elements making up the Type A dodecagon.