The aim is to find the distribution of vertices in successive shells, beginning with a vertex. This is the latest version, for fourteen rings.
- Code: Select all
ring count coordinates ( in ssf, base j7 = 2.61803398875)
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0, 1 1 0.0.0.0
1. 120 100 1.0.0.0 {3,3,5,5/2}, {3,5,5/2,5} {5,5/2,5,3}
10. 600 500 0.0.0.1 {4,3,3,5}, {5/2,5,3,3}, {4,10}
11. 720 600 0.f.0.0 {5,3,3,5}, {5,10}
f1. 3600 3000 f.0.1.0 {E,3,3,5}, {10,10}
100. 1440 1200 10.f.0.0
101. 6000 5000 0.1.f.0 f0.0.0.1 {3,5,3,3}
110. 9600 8000 1.f.0.f ff.1.0.0
111. 2520 2100 10.0.0.10 10f.0.0.0
f01. 14400 1.0000 10.10.0.1 f.0.f.f
f10. 4800 4000 f1.0.0.10 10.f.0.0
f11. 14400 1.0000 f1.f.0.f 0.f.1.10
ff1. 28800 2.0000 0.f0.1.1 f0.f.0.10 100.1.f.0 f.1.0.f0
1000. 3600 3000 10.0.f0.0
1001. 50400 3.6000 1.0.f.f0 1.11.10.0 10.f.10.1 ff.10.f.0
110.f.1.0 10.f1.0.f
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These coordinates are exact.
The first column, and the coordinates are given in base j7 = 2.61803398875&c. f is a digit representing j3=1.61803398875&c.
The second and third columns represent the count of vertices in that shell, given in decimal and twelfty.
A given shell contains one or more polytopes, expressed in the oblique coordinate system ssf. One treats every reflective region of the group [3,3,5] as a "possitive octant", with axies such that 1.0.0.0, 0.1.0.0, 0.0.1.0 and 0.0.0.1 correspond to x3o3o5o, o3x3o5o, o3o3x5o, and o3o3o5x, of edge 2. Rather like the standard cube is 1,1,1 in the group o2o2o.
One then gets many vertices which form the required polytopes. I put the thing up in the rippler, and it works as expected.