Rhombic icosahedron (RI) and rhombic triacontahedron (RT) relationship
Sándor Kabai
RI and RT relationship is shown here.
RI and RT relationship is shown here.
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Manipulatefi=GoldenRatio;alf=ArcTan[fi];bet=ArcTan[1/fi];bet1=ArcTan[1/fi^2];rtx=Cos[alf];rty=Sin[alf];y=Sin[alf];diap=N
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;diao=N6
5
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;prGR=PolyhedronData["AcuteGoldenRhombohedron","Faces"];obGR=PolyhedronData["ObtuseGoldenRhombohedron","Faces"];ri=PolyhedronData["RhombicIcosahedron","Faces"];rt=PolyhedronData["RhombicTriacontahedron","Faces"];rh=PolyhedronData["RhombicHexecontahedron","Faces"];p=N[rty/Cos[2Pi/20]];s=N[pSin[2Pi/20]];d=N[rty/Sin[2Pi/10]/2];h=Sqrt[1-p^2];eps={bet-bet1};p1=Translate[prGR,{0,0,diap/2}];ob1=Rotate[Translate[obGR,{0,0,-diao/2}],-bet+bet1-Pi/2,{0,1,0}];ob5=Table[Rotate[Translate[ob1,{-fly2+(-p-2s),0,1.344}],i2Pi/5,{0,0,1}],{i,5}];riup=Translate[ri,{0,0,2diao+1+fly1}];p5top=Table[Rotate[Rotate[p1,alf-bet1,{0,1,0}],i2Pi/5,{0,0,1}],{i,5}];Graphics3D[{{Pink,riup},Cyan,p5top,Yellow,ob5},ImageSize300,BoxedFalse,SphericalRegionTrue,ViewPoint{0,10,4},PlotRange{{-2.6,2.6},{-2.6,2.6},{-0.2,4.8}},ViewAngle0.1],{{fly1,1.6,"fly RI"},0,1.6},{{fly2,0,"fly obGR"},0,1.2},TrackedSymbols{fly1,fly2}6
5
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