Table[{Cos[k((2 Pi)/3)-(Pi/2)],Sin[k((2 Pi)/3)-(Pi/2)],0},{k,0,2}]

Table[{Cos[k((2 Pi)/3)-(Pi/2)+t],Sin[k((2 Pi)/3)-(Pi/2)+t],2},{k,0,2}]

Clear[SPpts,t];SPpts[t_]:={{0,-1,0},{((Sqrt[3])/2),(1/2),0},{-((Sqrt[3])/2),(1/2),0},{Sin[t],-Cos[t],2},{Cos[(π/6)+t],Sin[(π/6)+t],2},{-Cos[(π/6)-t],Sin[(π/6)-t],2}}

SPpts[Pi/6]

t=Pi/6;Graphics3D[{
{Opacity[0.5],Polygon[SPpts[t][[{4,5,6,4}]]],Polygon[SPpts[t][[{3,1,4,3}]]],Polygon[SPpts[t][[{1,2,5,1}]]],Polygon[SPpts[t][[{2,3,6,2}]]],Polygon[SPpts[t][[{3,6,4,3}]]],Polygon[SPpts[t][[{1,4,5,1}]]],Polygon[SPpts[t][[{2,5,6,2}]]]}
},
PlotRange->{{-1,1},{-1,1},{0,2}},Boxed->True,Axes->True,ImageSize->200
]

Clear[t]; Manipulate[
Graphics3D[{
{Opacity[0.5],Polygon[SPpts[t][[{4,5,6,4}]]],Polygon[SPpts[t][[{3,1,4,3}]]],Polygon[SPpts[t][[{1,2,5,1}]]],Polygon[SPpts[t][[{2,3,6,2}]]],Polygon[SPpts[t][[{3,6,4,3}]]],Polygon[SPpts[t][[{1,4,5,1}]]],Polygon[SPpts[t][[{2,5,6,2}]]]}
},
PlotRange->{{-1,1},{-1,1},{0,2}},Boxed->False,ImageSize->350
],
{{t,0},-Pi,Pi/3},ControlPlacement->Right
]

Plot[{Clip[2 (2/Pi) ArcSin[Sin[((Pi x)/4)]]]},{x,0,8},AspectRatio->Automatic]

Plot[{ Clip[2 (2/Pi) ArcSin[Sin[((Pi (x+2))/4)]]]},{x,0,8},AspectRatio->Automatic]

fSS[x_]:=Clip[2 (2/Pi) ArcSin[Sin[((Pi x)/4)]]];fSC[x_]:=Clip[2 (2/Pi) ArcSin[Sin[((Pi (x+2))/4)]]]

ParametricPlot[{fSC[t],fSS[t]},{t,0,8},PlotRange->{{-2,2},{-2,2}}]

ParametricPlot3D[{ fSC[t] fSS[s] ,fSS[t]  fSS[s] ,fSC[s]},{t,0,8},{s,0,4},PlotStyle->{Opacity[1]},PlotPoints->{121,121},Mesh->True,PlotRange->{{-2.2,2.2},{-2.2,2.2},{-2.2,2.2}}]

ParametricPlot3D[{(3+fSC[s])fSC[t],(3+fSC[s])fSS[t],fSS[s]},{t,0,8},{s,0,8},PlotStyle->{Opacity[1]},PlotPoints->{121,121},Mesh->True,PlotRange->{{-5.2,5.2},{-9.2,9.2},{-3.2,3.2}}]