Gerontocracy

I'm extremely interested in using slices of an object to implicitly reconstruct the object itself. Of course, this is most obviously useful for high-dimensional objects, but it can also lead to some interesting visualizations of low-dimensional objects. Here are a couple of examples.

Taking circle arc slices of an equilateral triangle isn't particularly interesting mathematically, but it still gives an interesting visual effect.

Here's the code:

cols = RGBColor /@ {"#118DF0", "#ECECDA", "#FF304F", "#0E2F56"}

Module[{polygonvertices, n},
 polygonvertices = {{0, 0}, {1, 0}, {1/2, Sqrt[3]/2}};
 n = 25;
 Manipulate[
  Graphics[{Thickness[.02], CapForm["Round"], 
    Flatten[Table[{cols[[i]], 
       Circle[polygonvertices[[i]], 
        r, {\[Pi] *2 (i - 1)/3, \[Pi] (2 i - 1)/3}]}, {r, s, 1.02, 
       1/n}, {i, 1, 3}], 1], EdgeForm[None], cols[[4]], 
    Polygon[{{3/2, 5}, {3/2, Sqrt[3]/2}, {1/2, Sqrt[3]/2}, {0, 
       0}, {-5, 0}, {-5, 5}}], 
    Polygon[{{1/2, 5}, {1/2, Sqrt[3]/2}, {1, 0}, {5, 0}}], 
    Polygon[{{0, 0}, {0, 1}, {-5, 1}, {-5, -5}, {5, -5}, {5, 1}, {1, 
       1}, {1, 0}}]}, 
   PlotRange -> {{-.1, 1.1}, {-0.16698729810778068`, 
      1.0330127018922193`}}, Background -> cols[[4]], 
   ImageSize -> 540], {s, 0., 1/n}]
 ]

(The stupid Polygon objects are to blank out the region outside the triangle. As already mentioned, I would be very happy to learn a better way to approximate the functionality of RegionFunction in a Graphics object.)