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

Unsupported Programs

Unsupported programs may be incomplete or of limited use and are provided for interest only

• dome_layer - dome strut arrangements
• twist - twist the edges of a polyhedron
• spidron - spidronise a polyhedron
• off2txt - convert an OFF file to Hedron format
• off_normals - utility for working with normals

General Documentation

• Antiprism Resource Files
• Named Colours in Antiprism
• Using edges in Antiprism
• OFF format description

Links to Complementary Programs

Using OFF format

• Geomview - 3D viewing and processing
• JavaView - 3D viewing and processing (Java)
• Springie (by Tim Tyler) - 3D viewing and processing (Java)
• Qhull - convex hulls and delaunay triangulation

Handling Antiprism Export Formats

• POV-ray - Persistence of Vision Raytracer using pov format
• VRML Viewers - Links to VRML viewers
• LiveGraphics3D - Java applet for 3D viewing using Mathematica format
• ImageMagick - Image processing, builds animations

Screenshots.

 

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