The 2nd-order tetractys is the third member of an infinite series of tetractyses, beginning with a mathematical point (0th-order tetractys), then the 1st-order tetractys, etc. The 10 1st-order tetractyses contains 85 yods, where

85 = 40 + 41 + 42 + 43.

Of these, 15 yods are corners of 1st-order tetractys and 70 yods are hexagonal yods, there being 7 such yods per 1st-order tetractys. 84 yods surround its centre, where

84 = 12 + 32 + 52 + 72.

13 yods line each side of the 2nd-order tetractys. This means that, when each of the n sectors of an n-gon are turned into 2nd-order tetractyses, there are (85−13=72) yods per sector, so that the number of yods in the n-gon = 72n + 1. They consist of (10n+1) corners of 1st-order tetractyses and 62n hexagonal yods. 62 is the number value of Tzadkiel, the Archangel of Chesed. The dodecagon (n=12) has 865 yods. Two separate dodecagons have 1730 yods, 1728 (=123) yods surrounding their centres. When they are joined together, 13 yods on one side of a dodecagon disappear, leaving (1730−13=1717) yods. (1717−13=1704) yods are outside their shared root edge, 852 yods in each dodecagon. (852−12=840) such yods surround the centres (denoted in the picture above by black dots) of the 12 sectors. Outside the root edge of the two joined dodecagons are (840+840=1680) yods that surround the (12+12=24) centres of their sectors. The (10+10) dodecagons that are part of the inner form of 10 Trees of Life have (8400+8400=16800) yods surrounding the 240 centres of their sectors. As the last of the regular polygons making up the inner form of the Tree of Life, the dodecagon has been shown in many pages of this website to embody the structural parameter 168 of the UPA as the number of turns in a half-revolution of a whorl. We now discover that, constructed from 2nd-order tetractyses, the dodecagons in 10 Trees of Life embody the structural parameter 16800 of the UPA as the number of turns in all its whorls. Single Trees represent single whorls, the 840 yods in each half of its inner form denoting the 840 turns in an outer or an inner half of the whorl, each half making 2½ revolutions around the axis of the UPA. The 10 whorls make 25 revolutions in the outer half of the UPA and another 25 revolutions in its core, i.e., 50 revolutions in total, showing how the Godname ELOHIM with number value 50 prescribes the form of the UPA as the subquark state of the E8×E8' heterotic superstring.

In terms of the correspondence between the Tree of Life and the 1st-order tetractys (see here), the hexagonal yod at the centre of a 1st-order tetractys corresponds to Malkuth. It signifies the physical level of manifestation of whatever holistic entity the tetractys represents. Similarly, the central 1st-order tetractys symbolises the Malkuth aspect of whatever entity the 2nd-order tetractys represents, whilst its central hexagonal yod denotes the Malkuth level of that aspect. In the case of the E8×E8' heterotic superstring, this yod denotes one of the 240 gauge charges of E8. What the 16800 yods surrounding the 240 centres of the dodecagons enfolded in 10 Trees mean is that these centres denote the gauge charges, which, spread along the 10 whorls, manifest in 4-d space-time as 16800 circularly polarised waves, being clockwise or anticlockwise according to whether the UPA is of the positive or negative type.