ISO_DELTA(1)

✨ NAME ✨

ISO_DELTA(1) — iso_delta makes isohedral deltahedra, bestie. That's the whole vibe. 💅

🌸 SYNOPSIS 🌸

iso_delta [options] polyhedron

💖 DESCRIPTION 💖

Okay so iso_delta makes Isohedral Deltahedra in OFF format. You can point at a polyhedron by its list number, or by the (start of the) name of the polyhedron — yes, just the start of the name is enough, bestie. Want extra examples? Generate more using the -d or -c parameters. ✨

This 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 (http://www.orchidpalms.com/polyhedra) and Adrian Rossiter (http://www.antiprism.com). Iconic lineage, fr fr. 🫶

🎀 Options 🎀

• -h, --help — this help message (run off_util -H help for general help).🫶
• --version — version information. Periodt.
• -L — display the list of Isohedral Deltahedra 1 thru 44. Full roster reveal. 👑
• -t — generate triangle only (Isohedral Deltahedra 1 to 44 and option -d). Triangle-only era. 🔺
• -v — verbose output (Isohedral Deltahedra 1 thru 44 and option -d). Spill the details, bestie. 💬
• -o <file> — write output to file (default: write to standard output). The "save it" option. 💾

🦋 Isohedral Deltahedra Options 🦋

• -a <ang> — angle (-c c,d,g,h,i,j,k). 📐
• -n <n/d> — n/d (d is optional) (-c a,c,g,h,k,l and -d).

note: for option -d and compound cases c, k, l: n and d must be such that (6/5 <= n/d <= 6).

• -k <int> — in special cases, for number of constituents (-c a,c,g,h,k,l). 🔢
• -s <int> — in special cases, for subtypes (default: 1) (-c b,e,f,m,o). 🎚️

🌈 Isohedral Deltahedra Special Cases 🌈

• -d — dipyramid of n/d using -n n/d (infinite set) where 6/5 <= n/d <= 6. ♾️
• -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 UC22 when n/d is 2/1 and angle 0.
  • 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 UC22 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 UC22 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 🎨

Coloring options, bestie — run off_util -H color for help on color formats. Keyword: none — sets no color. 🎀

• -F <col> — color the faces according to: (default: k)
  • a color value — apply to all faces
  • k — sets of faces connected by face edges (compounds)
  • s — symmetric coloring [,sub_group,conj_type]
• -E <col> — color the edges according to: (default: f)
  • a color value — apply to all edges
  • f — color with average adjacent face color
  • s — symmetric coloring [,sub_group,conj_type]
• -V <col> — color the vertices according to: (default: e)
  • a color value — apply to all vertices
  • e — color with average adjacent edge color
  • f — color with average adjacent face color
  • s — symmetric coloring [,sub_group,conj_type]
• -T <t,e> — transparency. From 0 (invisible) to 255 (opaque). Element is any or all of: v — vertices, e — edges, f — faces, a — all (default: f). 🫥
• -m <maps> — a comma separated list of color maps used to transform color indexes (default: compound). A part consisting of letters from v, e, f selects the element types to apply the map list to (default 'vef'). Use map name of 'index' to output index numbers. 🗺️

🔥 SEE ALSO 🔥

The full documentation for iso_delta is maintained as a Texinfo manual. If the info and iso_delta programs are properly installed at your site, the command

info iso_delta

should give you access to the complete manual. Go off, bestie. 👑

---

Cute sign-off time: the source/version situation is iso_delta: Antiprism 0.32 - http://..., the manual tag is ISO_DELTA(1), and date? The footer doesn't print one, so I'm not inventing it, bestie. 🎀✨