A pentagram is created by connecting the vertices of two pentagons of different sizes. If only a fifth part is created, then the illusion of interwoven pentagram can be produced. A real interwoven pentagram is made with sine waves.
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(*aandbaretheverticesofinternalandexternalpentagons,sizeratiofi^2*)​​fi=GoldenRatio;​​a=Table[{Sin[i2Pi/5],Cos[i2Pi/5],0},{i,6}];​​b=Table[{fi^2Sin[i2Pi/5+Pi/5],fi^2Cos[i2Pi/5+Pi/5],0},{i,6}];​​penta=Tube[a];​​pentb=Tube[b];​​Graphics3D[{penta,pentb},BoxedFalse,ImageSize300,SphericalRegionTrue,ViewPoint{0,0,100}]
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(*Veticesofpentagramselectedfromaandb*)​​starv={b[[1]],a[[2]],b[[2]],a[[3]],b[[3]],a[[4]],b[[4]],a[[5]],b[[5]],a[[1]],b[[1]]};​​start=Tube[starv,0.04];​​starp=Polygon[starv];​​​​Graphics3D[{Cyan,penta,Green,pentb,Pink,start,Yellow,starp},BoxedFalse,ImageSize300,SphericalRegionTrue,ViewPoint{0,0,100}]
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Graphics3D[{pentb,start,starp},BoxedFalse,ImageSize300,SphericalRegionTrue,ViewPoint{0,0,100}]
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​​(*One5thisdepictedandthenrepeated5times,producingtheillusionofinterwovenpentagram*)​​t=0.3;​​z=t/Cos[2Pi/20];​​a30=z-
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,0;​​z1=tTan[2Pi/20];​​a31=-z1+z-
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+t,0;​​x=tTan[2Pi/20];​​x1=t/Cos[2Pi/20];​​x10=t/Tan[2Pi/20];​​a32={-x10+2.4898,-0.8090+t,0};​​x3=tSin[2Pi/20];​​y=tCos[2Pi/20];​​a33=-x3+
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-y,0;​​​​m1=Polygon[{b[[1]],a30,a31,a32,a33,a[[1]]}];​​Graphics3D[{penta,start,Yellow,m1},BoxedFalse,ImageSize300,SphericalRegionTrue,ViewPoint{0,0,100}]​​
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m5=Table[Rotate[m1,i2Pi/5,{0,0,1}],{i,5}];​​Graphics3D[{Cyan,start,Yellow,m5},BoxedFalse,ImageSize300,SphericalRegionTrue,ViewPoint{0,0,100}]
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m5c=Table[{Hue[0.36^2i],Rotate[m1,i2Pi/5,{0,0,1}]},{i,5}];​​Graphics3D[{m5c},BoxedFalse,ImageSize300,SphericalRegionTrue,ViewPoint{0,0,100}]
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(*Partofasinwaveisselected*)​​sin1=ParametricPlot3D[{x,0,Cos[x]},{x,-Pi,2Pi}][[1]];​​sin2=ParametricPlot3D[{x,0,Cos[x]},{x,-Pi/2,3Pi/2},PlotStyle->{Pink,Tube[0.13]}][[1]];​​sn=Translate[sin2,{-Pi/2,0,0}];​​Graphics3D[{sin1,sin2},Axes->True,FaceGrids->All,ViewPoint->{0,-100,0},SphericalRegion->True]