Antiprism is a set of programs for generating, manipulating, transforming and visualising polyhedra.

Antiprism project is a suite of programs for the generation, manipulation, and visualisation of polyhedra.

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

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

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

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

Download.

Programs

Display

antiview - interactive OFF file viewer

Conversion

off2pov - converts OFF files to POV format
off2vrml - converts OFF files to VRML format
off2m - converts an OFF file to LiveGraphics3D 'm' format
off2crds - converts an OFF file to a coordinate file
m2off - converts a LiveGraphics3D 'm' file to OFF format

Manipulation

off_color - adds colours to an OFF file
off_trans - transformations (rotations, translations, etc) of OFF files
off_align - alignment of OFF files
off_util - utilities for OFF files (orientation, merging, etc)
planar - convert overlapping coplanar polygons into non-overlapping tiles

Reporting

off_report - report of global measures (e.g. area, volume, centroid), maxima, and counts
off_query - list element data

Generation

conv_hull - convex hulls (using Qhull)
pol_recip - polar reciprocals (duals)
geodesic - geodesic spheres
zono - zonohedra
polygon - polygon based polyhedra (prisms, pyramids, etc)
iso_delta - isohedral deltahedra
conway - Conway Notation transformations
poly_kscope - polyhedral kaleidoscope
unitile2d - makes uniform tilings on a surface
string_art - string figures
lat_grid - lattices and grids with integer coordinates
bravais - Bravais lattices
lat_util - lattice utilities
waterman - Waterman polyhedra
n_icons - sphericon like polyhedra
kcycle - kaleidocycle rings of polyhedron
jitterbug - jitterbug transformation
poly_weave - weave based on a polyhedron
canonical - canonicalize a polyhedron
sph_rings - rings of points on a sphere
sph_saff - spiral points on a sphere (Saff and Kuiljaars)
repel - equilibrium of points repelling on a sphere
minmax - minimise a spherical tesselation's maximum edge length, turn face data only into a spherical tesselation
col_util - colour utilities, plots and blending