SYMMETRO(1)

💖 SYMMETRO(1) 💖

okay so bestie, welcome to symmetro — the manual page is literally called SYMMETRO(1) and it lives in the User Commands section, and I'm about to make polyhedra sound as iconic as they actually are 🎀

✨ NAME ✨

symmetro — polyhedra with regular polygons at symmetry axes. yes that's the whole vibe. polygons. axes. symmetry. slay 💅

🌸 SYNOPSIS 🌸

symmetro [options]

🦋 DESCRIPTION 🦋

ok so here's the tea ☕ — Symmetrohedra and Twisters get created by placing equilateral polygons centered on the symmetry axes of Icosahedral, Octahedral, Tetrahedral, or Dihedral symmetry. that's the whole concept and it's giving geometry main character energy fr fr.

the sides of the polygons will be a multiple number of the axis reflection number. and the axes are numbered as 0, 1 and 2 — don't forget bestie.

it is possible to generate models such that the polygons intersect 👀. if a collision is detected, convex hull will be suppressed. not me warning you about polygon drama.

🚨 important!! options -k, -t, -s and -c cannot be used together but one needs to be specified. pick one. choose your fighter. periodt.

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🎀 Options 🎀

• -h, --help — this help message (run off_util -H help for general help). iconic of them to offer help ngl
• --version — version information. who are you, what version, etc 💁‍♀️
• -v — verbose output. she talks more. we love a chatty icon
• -l <lim> — minimum distance for unique vertex locations as negative exponent. (default: 12 giving 1e-12) like, precision bestie ✨
• -o <file> — write output to file (default: write to standard output). put it somewhere or let it fly free 🦋

👑 Program Options 👑

• -k <s,l,m,n,a> — Kaplan-Hart notation. Generate Symmetrohedra based on a study by Craig S. Kaplan and George W. Hart (http://www.georgehart.com). Url: https://cs.uwaterloo.ca/~csk/Old/projects/symmetrohedra/ Pdf: https://antiprism.com/misc/kaplan_hart_bridges2001.pdf
  • s: symmetry type of Symmetrohedra. sets {p,q,2}
    • I-icosahedral {5,3,2}
    • O-octahedral {4,3,2}
    • T-tetrahedral {3,3,2}
  • l,m,n: multipliers for axis polygons. Separated by commas, two multipliers may be * or 0, no more than two positive integers
  • a: face rotation type: vertex=1, edge=0 (default: 1)
  • example: -k i,2,*,4,e
• -t <s[p,q]i,m1,m2> — Twister notation. Generate twister models.
  • s: symmetry. I-icosahedral, O-octahedral, T-tetrahedral, D-dihedral
  • p,q: rotational order of each of the two axes. may be swapped
  • i: (default: 1): integer to select between non-equivalent pairs of axes having the same symmetry group and rotational orders
  • m1,m2: an integer multiplier for each axis. i.e. m1*p and m2*q
  • also can be entered as m1/d, m2/d fractional values e.g. T[3,2],1,2 I[5,2]2,1/2,3 D7[7,3],1,2 D11[2,2]5,2,2
  • Axis pairs are from the following:
    • T: [3,3], [3,2], [2,2]
    • O: [4,4], [4,3], [4,2]x2, [3,3], [3,2]x2, [2,2]x2
    • I: [5,5], [5,3]x2, [5,2]x3, [3,3]x2, [3,2]x4, [2,2]x4
    • Dn:[n,2], [2,2]x(n/2 rounded down)
• -s <n/d:D>,s — S symmetry twisters.
  • denominator d optional (default: 1)
  • optional D substitutes a polygon of n/D in place of n/d
  • optional s: symmetry override c - C symmetry
• -c <n1/d1:D1,n2/d2:D2,s,v> — C symmetry twisters
  • optional d denominator (default: 1)
  • optional D substitutes a polygon of n/D in place of n/d
  • optional n2 can differ from n1. if not specified n2=n1, d2=d1
  • optional s: symmetry: c - C (default), h - Ch, v - Cv, d - D
  • optional v: vertex index of radial polygon to bring to z plane
  • v of -1 is original position (default: index of largest z)
• -M <opt> — mirroring (may create compound). Can be x, y or z (default: none). she's reflective 💅
• -a <a,n> — a in degrees of rotation given to polygon applied to optional axis n (default: 0). A suffix of e may be used, where 1.0e is half the central angle of an edge. Then a is a multiplier. For example 2e. A suffix of x is like e but with a half turn offset
• -r <r,n> — set the edge length of the polygon on axis n (default: 0) to r. Must be non-negative. The default edge length is 1
• -A <a> — a in degrees is angle between axes (default: calculated)

🌈 Scene Options 🌈

• -C <mode> — convex hull. polygons=1, suppress=2, force=3, auto=4 (default: 4)
• -q <args> — include frame elements in output. r - rhombic tiling edges, a - rotation axes (default: none)
• -O <dist> — amount to offset the first polygon to avoid coplanarity with the second polygon, for example 0.0001 (default: 0.0)
• -x — remove any free faces that are produced

🎨 Coloring Options 🎨

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

• -F <col> — color the faces according to: (default: i)
  • a color value - apply to all faces
  • n - color by number of sides
  • s - symmetric coloring [,sub_group,conj_type]
  • i - color by axis number
• -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: axes), 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
  • axes: red,blue,yellow,darkgreen
    • note: position 4 color is for faces added by convex hull
  • kaplan: approximating colors in the symmetrohedra pdf file
  • colorful: red,darkorange1,yellow,darkgreen,cyan,blue,magenta,white,gray50,black (default when -F n)
  • (default internal maps shifted '+-3' when -F n)
• -D — don't cover digons with edge color
• -Q <col> — frame color (default: skyblue3)

💜 SEE ALSO 💜

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

info symmetro

should give you access to the complete manual. go read it bestie, it's giving ✨ full documentation ✨

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okay that's the whole thing!! this was symmetro from Antiprism 0.32 at http://w... and the date on the original footer was SYMMETRO(1) — anyway ily, go make some gorgeous polyhedra, and remember: no cap, the polygons are the moment 🫶💖🌟