Manipulate[nstra=Min[((Log[rtot])/(Log[(1/(Cos[ϕ °]+Sin[ϕ °]))]-0.001)),200];δ=(3/nstra);rtot=0.001;Graphics3D[{{Opacity[op],Table[Rotate[Cuboid[{-((((1/(Sin[ϕ °]+Cos[ϕ °]))))^k),-((((1/(Sin[ϕ °]+Cos[ϕ °]))))^k), δ k},{((((1/(Sin[ϕ °]+Cos[ϕ °]))))^k),((((1/(Sin[ϕ °]+Cos[ϕ °]))))^k), δ (k+1)}],k ϕ °,{0,0,1}],{k,0,Floor[nstra]}]}},PlotRange->{{-1,1 },{-1,1 },{0,3}},Axes->False,ImageSize->540,Boxed->False],
Column[{
Row[{Control[{{ϕ,6, "rotation angle"},0,90}],"  ",Dynamic[PaddedForm[ϕ,{3,1}] ],"°"}],
Control[{{op,0.92, "opacity"},0,1,Appearance->"Labeled"}]
}]]