Example: Compound of a Cube and Octahedron

The example is used to present a variety modelling techniques. A short way of making the model is given at the end.

1. Make a cube

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

   unipoly cube > cube.off

Display with

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

2. Make the dual octahedron

pol_recip is used for making duals by polar reciprocation.

To make a nice compound the radius of the sphere used for reciprocation needs to be the distance from the cube centre to the mid-point of an edge, and the sphere centre must be the centre of the cube.

unipoly has centred the cube on (0, 0, 0), but pol_recip will find this appropriate reciprocation centre by default. The radius can be specified using the -r option and passing two adjacent vertex index numbers of the cube. Again, pol_recip will find the appropriate radius by default, but for this example the radius will be specified in the command.

You can use off2pov with the -n option to display the cube with its vertex numbers.

   off2pov -x f -n -o cube.pov cube.off
   povray +a +p cube.pov

If you have antiview available then that is the easier option

   antiview -x f -n v cube.off

Vertices 3 and 5 are adjacent, so make the dual octahedron like this, and display it.

   pol_recip -r 3,5 cube.off > oct.off
   off2pov -o oct.pov oct.off
   povray +a +p oct.pov

3. Merge the polyhedra

OFF files are merged with off_util

   off_util cube.off oct.off > cub_oct.off

Display the result.

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

4. Use colours

To make it clearer that this is a compound of a cube and octahedron the two polyhedra could be given different colours using off_color.

Colour the cube faces red, and the octahedron faces green. The colours can be given as values, or by their colour names.

   off_color -f 1.0,0.0,0.0 cube.off > red_cube.off
   off_color -f green oct.off > green_oct.off

Now merge and display as before, this time making the edge and vertex elements smaller than the defaults

   off_util red_cube.off green_oct.off > color_cub_oct.off
   off2pov -v 0.02 -e 0.016 -o color_cub_oct.pov color_cub_oct.off
   povray +a +p color_cub_oct.pov

5. A shorter way to make the model

The cube is included as a resource model called cube. The pol_recip defaults are just right for this model. off2pov accepts multiple off files so there is no need to merge them.

The model and ray-traced image can be made with

   off_color -f red cube > cube_red.off
   pol_recip cube | off_color -f green > oct_green.off
   off2pov -v 0.02 -R 20,10,0 -o color_cub_oct.pov cube_red.off oct_green.off
   povray +a +p color_cub_oct.pov

Next: Example: Icosahelix
Up: Examples Using the Programs

Contact: adrian@antiprism.com - Modified 4.1.2008