Here's a similar idea, with different coding, and a dynamic clock to animate the morphing:
CirclePoints[{1., Pi/2}, 3*25] //
{Join @@ MapThread[Most@*Subdivide, {#, RotateLeft@#, #2 {1, 1, 1}}] &[CirclePoints[{1., Pi/2}, 3 ], Length@#/3], #} & //
Graphics[
GraphicsComplex[
{Cos[Clock[Infinity]], Sin[Clock[Infinity]]}^2 .# // Dynamic,
{EdgeForm[Thick], White, Polygon@Range@Length@First@#}
],
PlotRange -> 1.02] &