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**The Sri
Yantra**

All possible transformations of the mathematical (Yang-Mills) fields whose spin-1 quanta mediate
the forces between particles belong to a symmetry group. There are four types of such Lie groups, along with five
'exceptional groups'. The largest of the exceptional groups is the rank-8 Lie group called 'E_{8}'. It is
characterized by **248** roots, mathematically represented by 8-dimensional root vectors
expressed as 8-tuples of the numbers 0, ±½ & ±1 (see diagram opposite). Eight are so-called 'zero roots,' or
simple roots, and 240 are 'non-zero roots.' Associated with each root is a 10-dimensional, Yang-Mills gauge field.
E_{8}×E_{8} heterotic superstring theory predicts that **248** gauge bosons
(spin-1 particles) mediate the interactions between superstrings of ordinary matter in 10-dimensional space-time.
E_{6} is an exceptional subgroup of E_{8} that physicists have considered as an
intermediate stage in the breakdown of the symmetry of E_{8} to U(1)×SU(2)×SU(3), the symmetry group
of strong and electro-weak interactions that is the basis of the Standard Model of particle physics.
E_{6} has 78 roots, of which six are simple and **72** are non-zero roots. The
primary division:

240 = **72** + **168**

displayed in the properties of sacred geometries (see under the heading "240 =
**72** + **168**" in **The holistic pattern**) expresses the
fact that they embody E_{8}, whilst equally holistic subsections of these geometries embody its
exceptional subgroup E_{6}. It appears in the types of 8-tuples representing the 240 non-zero roots of
E_{8} shown in the diagram opposite.

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