pg_geo.py

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The polyhedron can be chosen with the -p option. The choices are

• t - regular tetrahedron
• o - regular octahedron
• i - regular icosahedron.

The type of face division is chosen with the -d option

• 1 - Class I (Alternate)
• 2 - Class II (Triacon)

Here are some example images (all Class I divisions).

pg_geo.py -p o 8 8 frequency spherical octahedron	pg_geo.py 10 10 frequency spherical icosahedron	pg_geo.py -l 10 10 frequency icosahedron projected onto a sphere	pg_geo.py -l -f 10 10 frequency icosahedron

In the 10 frequency icosahedral distributions the ball size shown is the maximum it can be without any balls overlapping (i.e the closest balls are in contact).

You can see how applying the frequency division to the spherical icosahedron produces a better distribution than applying it to the flat-faced icosahedron and then projecting the points onto a sphere.

Here are larger examples of spherical icosahedra, showing the different division types. They have the same orientation relative to the base icosahedron.

pg_geo.py -d 1 14 14 frequency Class I	pg_geo.py -d 2 16 16 frequency Class II

Program Help

usage: pg_geo.py [options] [freq]
         
Create coordinates for a higher frequency, plane-faced or spherical,
icosahedron, octahedron or tetrahedron. freq is the number of
divisions along an edge (default 4). By default the edges are divided
into sections with an equal angle at the origin, and the points are
then projected onto a sphere with a Class I division.

options
   -h       this help message
   -p poly  type of poly: i - icosahedron (default), o - octahedron,
            t - tetrahedron.
   -f       keep flat-faced polyhedron rather than projecting the points
            onto a sphere.
   -l       divide the edges by equal lengths rather than equal angles       
   -d type  type of face division,  1 (Class I, default) or 2 (Class II).
   -o file  write output to file, if this option is not used
            the program writes to standard output.