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The dodecagon and the radius
When we open from the midpoint twelve angles of 30° each and connect all the intersections with the circumference with each other we see that circle and dodecagon fit each other. We get a regular figure with lines that converge again in the center.
In other words, the dodecagon functions in an integral way with its center, radius and circumference. Each angular point is connected to all other angular points. Therefore this regular body can be considered to be an expression of – as well as an instrument for – the Self.
fig. 25.4.1 The dodecagon with its inscribed regular bodies
By drawing five midpoint angles of 72° each, we divide the circumference in five equal parts. The result is a pentagram. In this figure also the pentagram fits with the circle as a whole. However, in contrast to the dodecagon, in this star figure, there is not one point at the circumference that is connected to all other points.
fig. 25.4.2 The pentagram with further inscribed pentagrams
A different interconnection
In this case, the connection between the star points is realized, as it were, by a continuous line repeatedly ‘crossing over’ within the figure, always skipping one point. None of the resulting line segments returns from the circumference back to the center. Even when we try to get closer to the center by drawing ever smaller inscribed pentagrams within the original pentagram, their lines will never actually reach the center. For understanding the pentagram’s inherent identity, this is a significant fact. (25.4.a)
So with a midpoint angle of 72°, there is no echo rebounding from the circumference to the Self that it might use for the purpose of reconsidering, mirroring, retracting or reattuning itself. Apparently, the regular body of the pentagram is not intended as a reaffirmation of the Self .
Consequently, this regular body, although related to the center and connected to the circumference through its chords, does not play a role in our Self-development. Yet it advances through the figure without interruption.
A different category
The aspects based on a midpoint angle of 30° are not only situated on their chord but also lead back to the center by way of the radius. They are therefore based on two principles simultaneously, the chord and the radius. This implies that they have a twofold possibility of application, either passing through the Self or by-passing the Self.
As the pentagram lacks an integrated interplay of center, radius and circumference, there is no projection via an intermediary here. The aspect angles of the pentagram are based only on the chord.
The pentagon and the chord
This means that the 72° aspect does not have a reflective role and therefore does not induce Self-awareness. Its chord, as representative of the Center, operates imperatively, that is, in an undivided way, bypassing the person. These aspects belong to a different category and have a different kind of influence (25.4.c).
This implies that the aspects based on a midpoint angle of 30° or a multiple thereof, also belong to a category of their own, which for convenience’s sake we will call centripetal aspects. Within that group, we can further distinguish the major and minor aspects. Between these two subgroups, too, there is an essential difference.