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**17. The pair of Type C dodecagons embodies the number of
edges of the 4 _{21} polytope**

Each half of the 4 |
Constructed from Type B triangles, each of the two Type C dodecagons has 336 corners, sides & triangles surrounding its centre. |

A Type C polygon has Type B triangles as its sectors. Apart from their shared centre, there are
five corners, 14 sides & nine triangles per sector, i.e., 28 geometrical elements. Surrounding the centre of
the Type C dodecagon are (12×28=336) geometrical elements. They comprise [12×(5+9)=**168**] corners
& triangles and (12×14=**168**) sides. This
**168**:**168** division is characteristic of holistic systems displaying this
parameter, e.g., the 336 yods lining the 126 sides of the 42 triangles surrounding the centre of the 3-dimensional
Sri Yantra consist of **168** yods on the sides of the **21** triangles in each
half of it. (336+336=672) geometrical elements surround the centres of the two separate Type C dodecagons as 336
sides and 336 corners & triangles. This property is the counterpart of the 672 yods intrinsic to each set of
seven enfolded Type B polygons and surrounding their centres that was discussed in #12. It is also the counterpart of other sacred geometries previously
analysed. However, unlike yods, the number 10 cannot be meaningfully assigned to lines and triangles. Instead,
we must remember that — as considered earlier for the Type B polygons — 10 overlapping Trees of Life can
represent the single Tree composed of 10 Sephiroth. Surrounding the centres of the 20 separate, Type C
dodecagons that are part of their inner form are 6720 geometrical elements (3360 sides, 3360 corners &
triangles). As a holistic system in itself, the pair of Type C dodecagons through the 10-fold Tree of Life
generates the number 6720. This is the number of edges in the 4_{21} polytope whose vertices
determine the roots of E_{8}, which is the exceptional Lie group that describes the unified symmetry of
superstrings whose 10 dimensions are mapped by these 10 Trees of Life.

The 12th dodecagonal number is 672 (see Table 2 here). This is the number of geometrical elements surrounding the centres of the two Type C dodecagons.

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