n=30
gram=IdentityMatrix[3n+2]//MatrixForm
regularcoords=ConstantArray[0,{3,3n+2}]//MatrixForm
(*Order is X, Y, R
1-n ring
n+1 inner 
n+2 outer
n+3-2n+2 inner dual
2n+3-3n+2 outer dual*)
For[i=0,i<n,i++,regularcoords[[1,1,i+1]]=Cos[2Pi*i/n];regularcoords[[1,2,i+1]]=Sin[2Pi*i/n];regularcoords[[1,3,i+1]]=Sin[Pi/n]]
regularcoords[[1,3,n+1]]=1-Sin[Pi/n]
regularcoords[[1,3,n+2]]=-1-Sin[Pi/n]
For[i=0,i<n,i++,regularcoords[[1,1,i+n+3]]=(Sec[Pi/n]-Tan[Pi/n])Cos[(2 i+1)Pi/n];regularcoords[[1,2,i+n+3]]=(Sec[Pi/n]-Tan[Pi/n])Sin[(2 i+1)Pi/n];regularcoords[[1,3,i+n+3]]=(Sec[Pi/n]-Tan[Pi/n])Sin[Pi/n]]
For[i=0,i<n,i++,regularcoords[[1,1,i+2n+3]]=(Sec[Pi/n]+Tan[Pi/n])Cos[(2 i+1)Pi/n];regularcoords[[1,2,i+2n+3]]=(Sec[Pi/n]+Tan[Pi/n])Sin[(2 i+1)Pi/n];regularcoords[[1,3,i+2n+3]]=(Sec[Pi/n]+Tan[Pi/n])Sin[Pi/n]]
Graphics[{Table[Circle[{regularcoords[[1,1,i]],regularcoords[[1,2,i]]},Abs[regularcoords[[1,3,i]]]],{i,Length[regularcoords[[1,1]]]}]}]

regularcoords