Example: Compound of a Cube and Octahedron

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), which is the default centre for pol_recip. The radius can be specified using the -R option and passing two adjacent vertex index numbers of the cube. Use off2pov with the -n option to display the cube with its vertex numbers.

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

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_merge

   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.

   off_color -f 1,0,0 cube.off > red_cube.off
   off_color -f 0,1,0 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

Next: Example: Icosahelix
Up: Examples Using the Programs

Contact: adrian@antiprism.com - Modified 18.12.2005