[u]Direction vectors of Red- and Green-strut[/u][br][br]v1 = (cos(α),sin(α),0)[br]v2 = M5 v1[br][br][u]Find angle α such that z(v2)=0[br][/u][br]z(v2) = (ϕ-1)/2*cos(α) - 1/2*sin(α) = 0[br] (ϕ-1)*cos(α) = sin(α)[br] tan(α) = ϕ-1[br] α = arctan(ϕ-1)[br][br]cos(α) = cos(arctan(1/ϕ))[br] = ϕ/sqrt(2+ϕ)[br][br]sin(α) = sin(arctan(1/ϕ))[br] = 1/sqrt(2+ϕ)[br][br][u]Calculate intersection of strut-planes[/u] [br][br]Normal strut1 = (1,-ϕ,0)[br] [br]Rotate 72° around P5Axis: [br]M5 = {{1,ϕ,ϕ-1}, {-ϕ,ϕ-1,1}, {ϕ-1,-1,ϕ}} / 2[br]Normal strut2 = M5(-1,ϕ,0)[br] = (-1+ϕ^2,ϕ+ϕ^2-ϕ,1-ϕ-ϕ)/2[br] = (ϕ,1+ϕ,1-2ϕ)/2[br][br]plane1= ( 1*x - ϕ *y = 0)[br]plane2= ( ϕ*x +(1+ϕ)*y + (1-2ϕ)*z = 0)[br][br]v12 = ( 1,-ϕ,0) ⊗ (ϕ,1+ϕ,1-2ϕ)[br] = ( ϕ+2 , 2ϕ-1, 2ϕ+2)[br][br]|v12| = sqrt((ϕ+2)^2 + (2ϕ-1)^2 + (2ϕ+2)^2 )[br] = sqrt( 17ϕ+18 )[br][br][u]Normalized vectors of red-strut endpoints[/u][br][br]S1 = ( ϕ+2, 2ϕ-1, 2ϕ+2) / sqrt(17ϕ+18)[br]S2 = (-ϕ-2, 1-2ϕ, 2ϕ+2) / sqrt(17ϕ+18)

[b]Setup Script[/b][br][br]ϕ = (sqrt(5)+1)/2[br]O = (0, 0, 0)[br]S1 = ( ϕ+2, 2ϕ-1, 2ϕ+2)/sqrt(17ϕ+18)[br]S2 = (-ϕ-2, 1-2ϕ, 2ϕ+2)/sqrt(17ϕ+18)[br][br]cyl = Cylinder(S1, S2, 0.075)[br]L1cyl = Zip(Rotate(cyl, k*2pi/5, Line(O,(ϕ,1,0))),k,0..5)[br]L2cyl = Rotate(L1cyl, 2pi/5, Line(O, (1,0,ϕ)) )[br]L3cyl = Rotate(L2cyl, 2pi/5, Line(O, (1,0,ϕ)) )[br]L4cyl = Rotate(L3cyl, 2pi/5, Line(O, (1,0,ϕ)) )[br]L5cyl = Rotate(L4cyl, 2pi/5, Line(O, (1,0,ϕ)) )[br]L6cyl = Rotate(L5cyl, 2pi/3, Line(O,(ϕ-1,ϕ,0)))