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Mathematicians are familiar with a class of integers that they call "perfect numbers." These are positive integers whose divisors (including the trivial number 1 but excluding the perfect number itself) add up to themselves. The first perfect number is 6 because:

1 + 2 + 3 = 6,

where 1, 2 & 3 are its divisors. The second perfect number is 28 because:

1 + 2 + 3 + 4 + 5 + 6 + 7 = 28

and 1, 2, 3, 4, 5, 6 & 7 are its divisors. The third perfect number is
**496** because

1 + 2 + 4 + 8 + 16 + **31** + **62** + 124 +
**248** = **496**,

where 1, 2, 4, 8, 16, **31**, **62**, 124 &
**248** are its nine divisors. This means that, if the number **496** is
assigned to the centre of a tetractys, its nine divisors can be assigned to the nine yods that surround it. As the
centre of a tetractys symbolizes Malkuth, the last Sephirah of the Tree of Life, whose gematria number value is
**496** (see here), the tetractys pattern of this number is very apt!

The dimension of E_{8}×E_{8} is **496**. The dimension
**248** of each Lie group E_{8} is the sum of the first eight divisors of
**496**:

1 + 2 + 4 + 8 + 16 + **31** + **62** + 124 =
**248**.

As **31** = 2^{5} − 1, **62** =
2×**31** = 2(2^{5} − 1) = 2^{6} – 2, and 124 =
2×**62** = 2(2^{6} − 2) = 2^{7} – 4,

**248** = 2^{3} + (2^{4} + 2^{5} +
2^{6} + 2^{7}) = 8 + 240,

and

**496** = 2×**248** = 2^{4} +
(2^{5} + 2^{6} + 2^{7} + 2^{8}) = 16 + 480.

We see that the number 240 is the sum of *four* consecutive powers of 2, starting with
the power 4:

240 = 2^{4} + 2^{5} + 2^{6} + 2^{7}.

This demonstrates how the Pythagorean Tetrad (4) determines the number 240, which is a parameter of holistic systems, being:

1. the number of hexagonal yods in the seven regular polygons of the inner Tree of Life (see
here);

2. the number of yods in the 1-tree other than its SLs (see here);

3. the number of hexagonal yods in the faces of either the first three Platonic solids, the icosahedron or the
dodecahedron (see here);

4. the number of geometrical elements in the 2-dimensional Sri Yantra that surround its centre (see here).

The reason for this is that E_{8} has 240 roots, each associated with a gauge
charge and spin-1 field that transmits part of the superstring force. These roots are the counterparts of the yods
or geometrical elements in these sacred geometries, thereby illustrating the holistic/sacred geometrical nature of
the E_{8}×E_{8} heterotic superstring, as opposed to the SO(32) heterotic superstring, whose
symmetry group has **496** roots among which 240 roots are not differentiated.

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