# [GIF] Isotomic (Isotomic conjugates of edge parallels)

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 IsotomicAs in Isogonal, I'm taking edge parallels of triangles which are translating parallel to themselves and applying a conjugation operation, this time isotomic conjugation. I really wanted to have a gradient in the background rather than a solid color, but there was no way to do it without the resulting GIF begin over 6 MB, which is just too big.Here's the code for producing the GIF: SideVectors[Δ_] := (#[[2]] - #[[1]]) & /@ Transpose[{Δ[[1]], RotateLeft[Δ[[1]]]}]; SideLengths[Δ_] := Norm /@ SideVectors[Δ]; BarycentricCoords[Δ_, t_] := Sum[t[[i]] Δ[[1, i]], {i, 1, 3}]/Total[t]; TrilinearCoords[Δ_, {α_, β_, γ_}] := Module[{a, b, c}, {a, b, c} = SideLengths[Δ]; BarycentricCoords[Δ, {α a, β b, γ c}] ]; hexagons = Module[{cols = RGBColor /@ {"#14FFEC", "#DDDDDD", "#0D7377", "#212121"}, n = 12, th = .0025, pts = CirclePoints[{1, -π/6}, 6], triangles}, ParallelTable[ triangles = Prepend[Table[Triangle[pts[[{i, i + 1, Mod[i + 2, 6, 1]}]]], {i, 1, 5, 2}], Triangle[pts[[;; ;; 2]]]]; Show[ Table[ ParametricPlot[ TrilinearCoords[triangles[[k]], RotateLeft[1/SideLengths[triangles[[k]]]^2*1/{i + s/n, (1 - i - s/n) t, (1 - i - s/n) (1 - t)}, j]], {t, .00001, .99999}, PlotStyle -> Directive[CapForm[None], Thickness[th], Opacity[.5], cols[[1]]], ImageSize -> 540, Axes -> False, PlotRange -> 4/3], {k, 1, Length[triangles]}, {j, 0, 2}, {i, 0., 1 - 1/n, 1./n}], Graphics[{ FaceForm[None], EdgeForm[Directive[JoinForm["Round"], Thickness[.006], Darker[cols[[1]], .05]]], Polygon[pts], triangles[[1]]}], Background -> Blend[cols[[3 ;;]], .85]], {s, .001, 1, 1/60}] ]; Export[NotebookDirectory[] <> "hexagons.gif", hexagons, "DisplayDurations" -> {1/24}]