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Usage: wythoff [options] [input_file] Read a file in OFF format and apply a specified pattern to generate polygon tiles. The polyhedron faces are divided by a 'meta' operation into triangles each having vertices which are a vertex V, edge centre E and face centre F. A start point is positioned on one of these triangles, the next point is found by using the pattern to step between triangles, leading to a circuit. If input_file is not given the program reads from standard input. Options -h,--help this help message (run 'off_util -H help' for general help) --version version information -p <pat> pattern in form: [Coords0:Coords1:...]Path0,Path1... Coordinates are barycentric, in form aVbEcF: VEF element letters, and a,b,c are barycentric coordinates corresponding to the following element letter. Ommiting a an element letter and coordinate sets the coordinate to zero. Ommitting just the coordinate sets the coordinate to 1. E.g V = (1,0,0), VE = (1,1,0), V2E3F = (1,2,3) Paths are in the form: TrisPidx0Move0Pidx1Move1... Tris: one of +-* (default +) indicating that paths should start for positive, negative or both kinds of triangles. Pidx: an index number of a point from the coordinates list Move: an operation for stepping to the next triangle, given as a series of characters from the following: _ - no move, stay on the same triangle v,e,f - step over side opposite V,E,F V,E,F - step two trianglesi, rotating about V,E,F, according to: V=ef, E=fv, F=ve Paths can start with either a move or a point, but cannot both start and end with a move -c <op> Conway polyhedron notation operator, or 'list' to list all available operators with their corresponding patterns -R reverse pattern, exchanges the signs of the start triangles -r relabel pattern, exactly three letters VEF written in any order e.g. EFV relabels the pattern as V->E,v->e,E->F,e->f,F->V,f->v -M input geometry is a 'meta' tiling, don't apply meta operation -i tiles are coloured by index number (default, colour by value) -u output only one example of each type of tile (one per path) -a add the 'meta'-transformed base -f <ht> lift the face centres by this height -q quiet, don't print report -o <file> write output to file (default: write to standard output)
wythoff -c list
wythoff -M -p [VEF]0V,0E,0F,0V0E0F schwarz_2_3_5p | antiview wythoff -M -p [V]0E,0F schwarz_2_3_5p | antiview wythoff -M -p [VE]0V,0E,0v0e schwarz_2_3_5p | antiview wythoff -M -p [VEF]0v0e,0e0f,0f0v schwarz_2_3_5p | antiview
wythoff -p [E]0V,0F cube | antiview
unitile2d -s t -w 8 -l 24 2 | wythoff -c s -M | antiview
Triangle tilings are created, by default, from the input model by the Conway 'meta' operation. This consists of all triangles that join a face centre to one of its vertices and a neighbouring edge centre. With regard to starting triangles, the meta triangle (Vn, En, F) is labelled -/black, and the meta triangle (Vn+1, En, F) is labelled +/white. Alternatively, with option -M the input will be considered to be a suitable triangle tiling, and must be 2-colourable and all the vertices of even order.
The output tiling will not necesarily be planar, or have equal edge lengths. The output of 'spherical' tilings can be processed with the canonical program.
In the final model, vertices are coloured according to which elements are involved in the pattern coordinates: V=0/red, E=1/green, F=2/blue, VE=3/yellow, EF=4/cyan, FE=5/magenta, VEF=6/grey. Faces are coloured according to their corresponding position in the pattern.
Some Conway operators produce an edge with the same centre as an original edge. A corresponding constructive notation operation must produce a digon for this edge, because it is a polygon that wraps the element, and not just the edge of an adjoining face.
As a consequence, the Conway seed corresponds to a constructive notation 'seed' operator which, when applied to a polyhedron, generates the original polyhedron, but with digons along the edges.
As element types on the base tiling are equivalent, constructive notation operations that can be transformed into each other by permuting the element types can also be considered equivalent. Some equivalent Conway notation operators expressed in constructive notation are: seed/dual/ambo, truncate/zip/expand, kis/needle/subdivide. Some operators are symmetric with respect to the element types, for example snub, meta and bevel.
wythoff -p [4V2E8F]0feEV0fe0E0V ico | antiview
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