The Teikemeier/Drasny Sphere

 

The Three Dimensional Prism

Below we see each of the layers of the three dimensional Teikemeier/Drasny prism.

6
 
Level 6
5
 
Level 5
4

A4 = {110110, 101101, 011011}

Level 4
3

A3 = {101010, 010101}

E1 = {110010, 101001}
E2 = {110100, 011001}
E3 = {101100, 011010}
E4 = {010110, 001101}
E5 = {100110, 001011}
E6 = {100101, 010011}

Level 3

2

A2 = {100100, 010010, 001001}

Level 2
1
 
Level 1
0
 
Level 0

Notice that Rotation Groups, which can be seen as describing Wave Sequences, feature significantly in this construction. Each distinct ring in each level forms one (or more) rotation groups. The follow table shows this.

Level
Ring
Rotation Group
Wave Sequence
6
111111

5
5in6

4
Outer
4in6
Middle
RisingWater
Centre
Rising Openness

3
Outer
3in6
Middle
Fire & Spark
Wind & Water
Centre
101010 wave

2
Outer
Two Ascending
Middle
Rising Fire
Centre
100100 wave

1
1in6

0
000000

The symbols on the surface of the structure match the symbols in the External Chorand Sphere, which means that all of the symbols within the volume, including the co-located groups, are formed from the Internal Chorand Sphere.

Possible Variations

There are a number of possible variations that could be considered for this structure.

Firstly, the order in which the symbols in Layer 1 are positioned around the circumference has a significant impact on the resulting structure. Which symbols are within the volume of the prism and which are on the surface in Layer 2 depends on which symbols are adjacent in Layer 1. Further, the symbols co-located as A2 in Layer 2 are determined by which symbols are diagonally opposite in Layer 1. Therefore, choosing a different order for the Layer 1 symbols results in a significantly different set of positions for the symbols in the final structure.

Chorand, Teikemeier and Drasny all, independently, chose the same circular order for the symbols in Layer 1. This is the simple linear order generated by rising a yang line through the yin background and it is the most obvious choice. Because this choice places the symbols in Layer 1 in the order in which they appear in their rotation group, the rest of the elements of the structure also form rotation groups, as described above.

One interesting variation would be to make diagonally opposite symbols in Layer 1 overturned opposites, rather than exchanged opposites. This would make the set A2 of co-located symbols

{100001, 010010, 001100}

instead of the set given above. This, in turn would shift the symmetry of other co-located symbols to overturning opposites, rather than exchanged opposites.

Also, although 000000/111111 are the natural choice for the polar symbols, it is possible to make other choices. I have previously analysed this possibility in the context of Chorand spheres. A similar variation in structure would be expected for this prism.

On the next page, I present some analysis of the sets of co-located symbols.