Antiprism Up Next
Home
Programs
Examples
Album
Download
Development
Forum
About

iso_delta - isohedral deltahedra

Usage    |    Examples    |    Notes

Usage



Usage: iso_delta [options] polyhedron

Make Isohedral Deltahedra in OFF format. The polyhedron may be specified
by its list number, or the (start of the) name of the polyhedron.
Additional examples can be generated using -d or -c paramters.
Based on a paper by G. C. Shephard
Periodica Mathematica Hungarica, Volume 39, Numbers 1-3, 2000 , pp. 83-106(24).
with enhancements by Jim McNeill (http://www.orchidpalms.com/polyhedra)
and Adrian Rossiter (http://www.antiprism.com)

Options
  -h,--help this help message (run 'off_util -H help' for general help)
  --version version information
  -l        display the list of Isohedral Deltahedra 1 thru 42
  -t        generate triangle only (Isohedral Deltahedra 1 to 42 and option -d)
  -v        verbose output (Isohedral Deltahedra 1 thru 42 and option -d)
  -o <file> write output to file (default: write to standard output)

Isohedral Deltahedra Options
  -a <ang>  angle
  -n <n/d>  n/d (d is optional)
              note: for option -d and compound cases c, g, h:
              n and d must be such that (2 < n/d < 6)
  -k <int>  in special cases, for specifying number of constituents
  -s <int>  in special cases, for subtypes (default: 1)

Isohedral Deltahedra Special Cases
  -d        dipyramid of n/d using -n n/d (infinite set)
  -c <type> compound cases (a thru f from Shephard's paper)
              a - tetrahedron repeated k times, evenly spaced
                     when k=1 tetrahedron, when k=2 Stella Octangula
                     Uniform Compound Set UC23 when n/d is 2/1
              b - 5 or 10 tetrahedra
                     s=1 icosahedral, s=2 with horizontal reflection
                     Uniform Compounds UC05 and UC06
              c - 2 dipyramids of n/d using -a angle (default: calculated)
                     relaxed dual of Uniform Compound Set UC20 and k=1
              d - 6 octahedra using -a angle (default: 22.5)
                     At 45.0 degrees is 3 Octahedra
                     dual of Uniform Compound Set UC07
              e - 4 or 8 triangular dipyramids
                     s=1 octahedral, s=2 with horizontal reflection
                     relaxed duals of Uniform Compounds UC30 & UC31
              f - 6 or 12 5/1 pentagonal or 5/2 star dipyramids
                     5/1: s=1 icosahedral, s=2 with horizontal reflection
                          relaxed duals of Uniform Compounds UC34 & UC35
                     5/2: s=3 icosahedral, s=4 with horizontal reflection
                          relaxed duals of Uniform Compounds UC36 & UC37

         additional cases:
              g - 2 tetrahedra using -a angle (default: 45.0)
                     At 45.0 degrees is Uniform Compound UC04
                     Uniform Compound Set UC23 when n/d is 2/1 and k=1
              h - 2 tetrahedra repeated k times, evenly spaced
                     using -a angle (default: 1.0)
                     Uniform Compound Set UC23 when n/d is 2/1 for any k
              i - 6 tetrahedra using -a angle (default: 45.0)
                     Uniform Compound UC01. At 45.0 degrees is UC03
              j - 12 tetrahedra using -a angle (default: 30.0)
                     Uniform Compound UC02. At 45.0 degrees is UC03
              k - 2 dipyramids of n/d repeated k times, evenly spaced
                     using -a angle (default: 1.0)
                     relaxed dual of Uniform Compound Set UC20
              l - k dipyramids of n/d using -n n/d, evenly spaced
                     relaxed dual of Uniform Compound Set UC21
              m - 10 or 20 triangular dipyramids
                     s=1 icosahedral, s=2 with horizontal reflection
                     relaxed duals of Uniform Compounds UC32 & UC33
              n - 6 10/3 star dipyramids
                     relaxed dual of Uniform Compounds UC41
              o - 5 or 10 Augmented Tetrahedra T2(1)
                     s=1 icosahedral, s=2 with horizontal reflection
                     relaxed duals of Uniform Compounds UC55 & UC56
              p - 5 Augmented Octahedra O6(1)
                     relaxed dual of Uniform Compounds UC57
              q - 5 Excavated Octahedra O6(2)
                     relaxed dual of Uniform Compounds UC58

Coloring Options (run 'off_util -H color' for help on color formats)
  -f <opt> compound coloring
              key word: none - sets no color (default: c)
              c - unique coloring for each constituent
              s - symmetric colouring (should always be one color)
  -T <tran> face transparency. valid range from 0 (invisible) to 255 (opaque)
  -m <maps> color maps for all elements to be tried in turn (default: compound)


Examples

View polyhedron number 9 in the list
iso_delta 9 | antiview


View 2 pairs of star-pentagon dipyramids at an angle of 3 degrees
iso_delta -c k -n 5/2 -k 2 -a 3 | antiview


Notes

iso_delta was written by Roger Kaufman.

It is based on a paper by G. C. Shephard Periodica Mathematica Hungarica, Volume 39, Numbers 1-3, 2000 , pp. 83-106(24) with enhancements by Jim McNeill and Adrian Rossiter.


     Next: iso_kite - isohedral kite-faced polyhedra
     Up: Programs and Documentation


Home   |   Programs   |   Examples   |   Album   |   Download   |   Development   |   Forum   |   About

Contact: adrian@antiprism.com      -      Modified 12.9.2016