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Usage: symmetro [options] Symmetrohedra and Twisters are created by placing equilateral polygons centered on the symmetry axes of Icosahedral, Octahedral, Tetrahedral, or Dihedral symmetry. The sides of the polygons will be a multiple number of the axis reflection number. Axes are numbered as 0, 1 and 2 It is possible to generate models such that the polygons intersect. If a collision is detected, convex hull will be suppressed options -k, -t, -s and -c cannot be used together but one needs to be specified Options -h,--help this help message (run 'off_util -H help' for general help) --version version information -v verbose output -l <lim> minimum distance for unique vertex locations as negative exponent (default: 12 giving 1e-12) -o <file> write output to file (default: write to standard output) 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) -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 -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)
Make a Cuboctahedron (U7)
symmetro -k o,1,1,0,e | antiview symmetro -t O[3,3],1,1 | antiview
symmetro -k o,1,1,0 -r 2 | antiview symmetro -t O[4,3],1,1 -r 2 | antiview
symmetro -k o,1,0,1 -a 28.53243959961367 -C f | antiview symmetro -t O[4,2],1,1 -a 28.53243959961367 -C f | antiview
symmetro -k t,1,1,0 -C s -a 15 | antiview symmetro -t T[3,3],1,1 -C s -a 15 | antiview
symmetro -s 5:2 -a 2e | antiview -v 0.03
symmetro -c 5,5,d | antiview
symmetro -c 5,5,h | antiview
symmetro -k t,2,3,*,e -F n -m kaplan | antiview symmetro -k o,2,3,*,e -F n -m kaplan | antiview symmetro -k o,3,2,*,e -F n -m kaplan | antiview symmetro -k i,2,3,*,e -F n -m kaplan | antiview symmetro -k i,3,2,*,e -F n -m kaplan | antiview symmetro -k t,1,2,*,v -F n -m kaplan | antiview symmetro -k o,1,2,*,v -F n -m kaplan | antiview symmetro -k o,2,1,*,v -F n -m kaplan | antiview symmetro -k i,1,2,*,v -F n -m kaplan | antiview symmetro -k i,2,1,*,v -F n -m kaplan | antiview
symmetro -k o,2,2,0,v -r 1.06680419358835388 -F n -m kaplan | antiview symmetro -k o,3,3,0,v -r 1.04966777114351 -F n -m kaplan | antiview -v 0.03 symmetro -k i,2,2,0,v -r 1.09818547139510914 -F n -m kaplan | antiview -v 0.03 symmetro -k i,3,3,0,v -r 1.0726110096817 -F n -m kaplan | antiview -v 0.05
symmetro -k t,2,0,3,e -F n -m kaplan | antiview symmetro -k t,2,0,3,v -F n -m kaplan | antiview symmetro -k o,1,0,2,v -F n -m kaplan | antiview symmetro -k o,3,4,*,e -F n -m kaplan | antiview symmetro -k o,3,4,*,v -F n -m kaplan | antiview symmetro -k o,*,2,3,e -F n -m kaplan | antiview symmetro -k o,*,2,3,v -F n -m kaplan | antiview symmetro -k i,3,5,*,e -F n -m kaplan | antiview symmetro -k i,3,5,*,v -F n -m kaplan | antiview symmetro -k i,2,*,5,e -F n -m kaplan | antiview symmetro -k i,2,*,5,v -F n -m kaplan | antiview symmetro -k i,*,2,3,e -F n -m kaplan | antiview symmetro -k i,*,2,3,v -F n -m kaplan | antiview
symmetro -k o,*,3,*,e -F n -m kaplan | antiview symmetro -k i,1,2,*,v -F n -m kaplan -r 1.07046626932,1 | antiview symmetro -k i,2,*,3,e -F n -m kaplan | antiview
symmetro -k i,2,2,*,1 -F n -m kaplan -r 2.03614784182,1 | antiview -v 0.03 symmetro -k i,2,1,*,1 -F n -m kaplan -r 1.9021130325885 | antiview -v 0.03 symmetro -k i,2,2,*,1 -F n -m kaplan | antiview -v 0.05 symmetro -k i,4,3,*,e -F n -m kaplan | antiview -v 0.07 symmetro -k i,2,3,*,1 -F n -m kaplan | antiview -v 0.05 symmetro -k i,2,3,*,1 -F n -m kaplan -r 1.583841856265,1 | antiview -v 0.05 symmetro -k i,2,4,*,e -F n -m kaplan | antiview -v 0.07 symmetro -k i,2,4,*,1 -F n -m kaplan -r 1.05398768021455,1 | antiview -v 0.07 symmetro -k i,3,1,*,1 -F n -m kaplan | antiview -v 0.07 symmetro -k i,3,2,*,1 -F n -m kaplan | antiview -v 0.07 symmetro -k i,*,2,2,1 -F n -m kaplan | antiview -v 0.07 symmetro -k i,*,1,4,e -F n -m kaplan | antiview -v 0.06 symmetro -k i,3,4,*,v -F n -m kaplan -r 1.5665309813,1 -l 8 | antiview -v 0.03 symmetro -k i,3,4,*,e -F n -m kaplan | antiview -v 0.06 symmetro -k i,3,5,0,v -F n -m kaplan -r 1.3159206178527,1 | antiview -v 0.03 symmetro -k i,4,2,*,e -F n -m kaplan | antiview -v 0.06 symmetro -k i,*,1,4,1 -F n -m kaplan | antiview -v 0.06 symmetro -k i,1,*,2,1 -F n -m kaplan | antiview -v 0.06 symmetro -k i,1,*,3,e -F n -m kaplan | antiview -v 0.06 symmetro -k i,2,*,3,1 -F n -m kaplan | antiview -v 0.06
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