Example: Icosahelix

The example is used to present a variety modelling techniques. For an easy way to make helixes from polyhedra see extras/python/helix.py in the Antiprism data directory, which bonds by face rather than vertex using off_align -F.

1. Make an icosahedron

This can be done with unipoly, which can be used to make all the uniform polyhedra.

   unipoly icosahedron > icosa.off

Display with

   off2pov -o icosa.pov icosa.off
   povray +a +p icosa.pov

2. Find faces to join

The icosahelix will be made by repeatedly copying the icosahadron and always bonding the same two faces together. The faces are specified by three index numbers. Use off2pov with the -n option to display the icosahedron with its vertex numbers.

   off2pov -x vf -n -o icosa.pov icosa.off
   povray +a +p icosa.pov

If you have antiview available then that is the easier option

   antiview -x f -n v icosa.off

Joining vertices 3,8,9 to 10,7,11 looks like it would make a nice helix.

3. Colour the icosahedron

Colour the icosahedron with off_color. It might be nice to give it a minimal proper colouring. It would have three colours with no two adjoining faces having the same colour. This can be done with -f P option.

   off_color -f P icosa.off > color_icosa.off

Display the result.

   off2pov -o color_icosa.pov color_icosa.off
   povray +a +p color_icosa.pov

Colours with a bit more contrast would be better. Instead of setting colour values use the -f P option (small p) to set colour indexes, which can be converted into colour values using a color map file.

Make a the file containing the following lines and call it colormap.txt

1 = 0.3 0.3 0.8
2 = 0.8 0.1 0.2
3 = 0.9 0.9 0.7

The first number is the index followed by three numbers ranging 0-1 for the colour value. The first number is the amount of red, then the amount of green, then the amount of blue. Using this file index 1 will be coloured bluish, index 2 reddish, and index 3 pale cream.

Colour the icosahedron again, this time using the colour map.

   off_color -f p icosa.off -m colormap.txt > color_icosa.off

Display it.

   off2pov -o color_icosa.pov color_icosa.off
   povray +a +p color_icosa.pov

4. Build the helix

The off_align program will align one polyhedron relative to another.

Copy color_icosa.off to icosahx.off to start the helix. Now join a copy of the icosahedron to the start of the helix. The -p option specifies the vertices that will be joined. The -Mi 2 option makes sure the new icosahedron is joined at the front of the file. This is so its vertex numbers won't change and then the command can be repeated to add the following icosahedra.

   off_align -p 3,8,9,10,7,11 -M 2 -b color_icosa.off -o icosahx.off icosahx.off

Repeat the command another ten times for a twelve icosahedron icosahelix.

Display the completed icosahelix.

   off2pov -o icosahx.pov icosahx.off
   povray +a +p icosahx.pov

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Up: Examples Using the Programs

Contact: adrian@antiprism.com - Modified 5.1.2008