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import math;
int n=8, skip=3;
pair r(int k) { return unityroot(n,k); }
pen col=blue, col2=purple;
guide square=box((1,1),(-1,-1));
guide step(int mult)
{
guide g;
for(int k=0; k<n; ++k)
g=g--r(mult*k);
g=g--cycle;
return g;
}
guide oct=step(1), star=step(skip);
guide wedge(pair z, pair v, real r, real a)
{
pair w=expi(a/2.0);
v=unit(v)*r;
return shift(z)*((0,0)--v*w--v*conj(w)--cycle);
}
filldraw(square, col);
filldraw(oct, yellow);
// The interior angle of the points of the star.
real intang=pi*(1-((real)2skip)/((real)n));
for(int k=0; k<n; ++k) {
pair z=midpoint(r(k)--r(k+1));
guide g=wedge(z,-z,1,intang);
filldraw(g,col2);
}
fill(star,yellow);
filldraw(star,evenodd+col);
size(5inch,0);
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