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zono - zonohedra from OFF files

Usage    |    Examples    |    Notes


Usage: zono [options] [star_file] 

Make a zonohedron or add zones to a convex seed polyhdron. The zones are
created from a star of vectors, which can be based on a polyhdron (input
model and option -m) or initialised (option -P) to make a polar zonohedron.
If input_file is not given the program reads from standard input

  -h,--help this help message (run 'off_util -H help' for general help)
  --version version information
  -m <mthd> method to create star from input, can be
               v - centre to vertices are vectors (default)
               a - all vertex to vertex are vectors
               i - implicit edges (face sides) are vectors
               e - explicit edges are vectors
  -c <cent> centre of points for method v, in form 'X,Y,Z', or C to use
            centroid (default '0,0,0')
  -s        output the star (instead of the zonohedron)
  -S <poly> seed model to add zones to, must be convex
  -u        make vectors unit length
  -C <col>  colour for new zone faces
  -P <arg>  polar zonohedron from ordered star, arg can be an offset polygon
            given as an integer or fraction (e.g. 5, 7/2) or 's' to use
            star_file. Optionally, follow by a comma and an integer to
            to make a spirallohedron with that spiral width (default:0, a
            polar zonohedron). Any further comma separated parts are colour
            maps to colour the faces.
  -T <star> translation surface made from two ordered stars (argument star
            and star_file) optionally followed by a comma and two characters
            (or one to use for both) to indicate if the stars of vectors
            are open, or close to form a loop: d-detect, c-force close,
             o-leave open.
  -o <file> write output to file (default: write to standard output)


See also, zono examples with images.

A largish polar zonohedron

zono -P 50 | antiview

A largish rhombic spirallohedron
zono -P 50,5 | antiview

Rhombic triacontahedron
zono ico | antiview

Non-Archimedean truncated octahedron
zono -m i ico | antiview

Archimedean truncated octahedron
zono -m i -u ico | antiview

Make a unit star from tetrahedron vertices and use to add red zones to a icosahedron
zono -S ico -u -C red tet | antiview

Rhombic torus as a translation surface
off_util -s std_pol10  | off_trans -R 90,0,0 | zono -T std_pol10 - | antiview

Spirallohedron from translation surface
off_trans -T 0,0,1 std_pol12  | off_util -Dv3- >
off_trans -T 0,0,1 std_pol12  | off_util -Dv-2 >
zono -T | poly_kscope -sC4 | antiview


Option -S implements George Hart's Zonish polyhedra.

Rhombic spirallohedra were discovered by Russell Towle. See also Spirallohedra Rule! and Hexagonal Spirallohedra,

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Contact:      -      Modified 27.5.2023