TETRA59(1)

✨ NAME ✨

okay so bestie, this is tetra59(1) from the User Commands manual — the header up top is TETRA59(1), and the name is tetra59: 59 tetrahedra with rational dihedral angles. it’s giving niche geometry icon energy — slay, no cap. 💖

🦋 SYNOPSIS 🦋

tetra59 [options] tetrahedron

💜 DESCRIPTION 💜

Generate 59 Tetrahedra with Rational Dihedral Angles in off format. The 59 Sporadic Tetrahedra is from a paper by Kiran S. Kedlaya, Alexander Kolpakov, Bjorn Poonen, and Michael Rubinstein: Space Vectors Forming Rational Angles. The paper can be found at: https://arxiv.org/abs/2011.14232. literally go read it if you’re obsessed. 📚

There are also two special infinite cases included in the findings. The first case was published by M.J.M Hill in 1895. The second case is new. periodt. ✨

🌸 Options 🌸

• -h,--help — this help message (run off_util -H help for general help)
• --version — version information
• -H — abstract from the paper and description of regge symmetry
• -L <opt> — list Sporadic Tetrahedra as i - integer, d - degrees, p - pairs
• -v <opt> — verbose output math: e - edges, f - faces, p - pairs, a - all
• -o <file> — write output to file (default: write to standard output)

🎬 Scene Options 🎬

• -d <mthd> — order of dihedral angles, for matching dihedral angle at position

term 1 (a12) for regge symmetry (also permutes special cases) angles permuted as pairs: 1-(a12,a34) 2-(a13,a24) 3-(a14,a23) for each pair in position one, there are two arrangements (a:1,2,3 b:1,3,2); (c:2,1,3 d:2,3,1); (e:3,1,2 f:3,2,1) (default:a) — it’s giving angle-order lore, iykyk.

• -p <int> — build regge pair if found (1 or 2) not for special cases (sets -z)
• -P <n,d> — force second pair of model number n, and method d (not with -p)
• -r — reflect
• -z — scale volume to 1

🧚 Special Cases 🧚

• -s <int> — special case 1 or 2 (default: none)
  • case 1: (pi/2, pi/2, pi - 2x, pi/3, x, x) for pi/6 < x < pi/2 (30 < x < 90 degrees)
  • case 2: (5pi/6 - x, pi/6 + x, 2pi/3 - x, 2pi/3 - x, x, x) for pi/6 < x <= pi/3 (30 < x <= 60 degrees)
• -a <ang> — angle in degrees (default: 45)
• -w — allow any angle for case s (for testing case 2, 60 < x < 90 which seems to yield a tetrahedron). not me being curious about the forbidden angle zone 🙈

🌈 Coloring Options 🌈

(run off_util -H color for help on color formats) keyword: none — sets no color

• -F <col> — color the faces according to: (default: u)
  • a color value — apply to all faces
  • u — unique color
  • s — symmetric coloring [,sub_group,conj_type]
  • r — regge group (1-16) (not for special cases) — main character energy fr fr
• -E <col> — color the edges according to: (default: lightgray)
  • a color value — apply to all edges
  • s — symmetric coloring [,sub_group,conj_type]
• -V <col> — color the vertices according to: (default: gold)
  • a color value — apply to all vertices
  • 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
  • compound: yellow,red,darkgreen,blue,magenta,cyan,darkorange1
  • rainbow16: (special map for -F r)

💖 SEE ALSO 💖

The full documentation for tetra59 is maintained as a Texinfo manual. If the info and tetra59 programs are properly installed at your site, the command

info tetra59

should give you access to the complete manual. fr fr, go get that full manual if you need more. 🫶

okay that’s the whole page, bestie. footer sign-off: source/version is tetra59: Antiprism 0.32 - http://ww..., the manual tag is TETRA59(1), and this footer does not print a date, so I’m not inventing one. bye! 💅✨