Sándor Kabai
Space filling around a rhombic hexecontahedron (RH)
Golden rhombic polyhedra are used around an RH in an attempt to create a space filling arrangement.
Space filling around a rhombic hexecontahedron (RH)
Golden rhombic polyhedra are used around an RH in an attempt to create a space filling arrangement.
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fi=GoldenRatio;alf=ArcTan[fi];bet=ArcTan[1/fi];bet1=ArcTan[1/fi^2];rtx=Cos[alf];rty=Sin[alf];y=Sin[alf];m=2yfi;p=N[rtx/Sin[2Pi/10]];d=N[pCos[2Pi/10]];h=N[2dSin[2Pi/10]];em=N1+-1-;prGR=GraphicsComplex[PolyhedronData["AcuteGoldenRhombohedron","VertexCoordinates"],Polygon[PolyhedronData["AcuteGoldenRhombohedron","FaceIndices"]]];obGR=GraphicsComplex[PolyhedronData["ObtuseGoldenRhombohedron","VertexCoordinates"],Polygon[PolyhedronData["ObtuseGoldenRhombohedron","FaceIndices"]]];rh=GraphicsComplex[PolyhedronData["RhombicHexecontahedron","VertexCoordinates"],Polygon[PolyhedronData["RhombicHexecontahedron","FaceIndices"]]];rt=GraphicsComplex[PolyhedronData["RhombicTriacontahedron","VertexCoordinates"],Polygon[PolyhedronData["RhombicTriacontahedron","FaceIndices"]]];rtn=Rotate[rt,Pi,{0,0,1}];ri=GraphicsComplex[PolyhedronData["RhombicIcosahedron","VertexCoordinates"],Polygon[PolyhedronData["RhombicIcosahedron","FaceIndices"]]];icov=PolyhedronData["Icosahedron","VertexCoordinates"];
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(*PutanRTonacentralRH*)rtup=Translate[rt,{0,0,fi^2}];rhrt={Cyan,rtup,Yellow,rh};Graphics3D[{rhrt},ViewPoint{0,100,0},ImageSize200,ViewAngle0.01,BoxedFalse,SphericalRegionTrue]
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icov=PolyhedronData["Icosahedron","VertexCoordinates"];rt12=Rotate[Map[Translate[rtn,#]&,m*icov],Pi,{0,0,1}];Graphics3D[{rt12},ViewPoint{0,100,0},ImageSize200,ViewAngle0.01,BoxedFalse,SphericalRegionTrue]
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Graphics3D[{Glow[White],EdgeForm[Thick],rt12},ViewPoint{0,0,100},ImageSize300,ViewAngle0.01,BoxedFalse,SphericalRegionTrue]
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(*PrepareaRH-RTtowerexpectedtobecomethebackboneofthestructure*)tower=Table[Translate[rhrt,{0,0,i(fi^3+1)}],{i,2}];Graphics3D[{tower,rt12},ViewPoint{0,100,0},ImageSize300,ViewAngle0.01,BoxedFalse,SphericalRegionTrue]
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tower5=Table[Rotate[Rotate[Rotate[{rhrt,tower},Pi,{0,0,1}],-2bet,{0,1,0}],i2Pi/5,{0,0,1}],{i,5}];Graphics3D[{rt12,rhrt,tower,tower5},ViewPoint{0,0,-100},ImageSize400,ViewAngle0.01,BoxedFalse,SphericalRegionTrue]
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(*Twokindsofframesarepreparedfromprolategoldenrhombohedra*)diap=N
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;prGRup=Translate[prGR,{0,0,diap/2}];prGRtilt=Table[Rotate[Rotate[Rotate[prGRup,Pi,{0,0,1}],2bet1,{0,1,0}],i2Pi/3,{0,0,1}],{i,3}];prGRtilt1=Table[Rotate[Rotate[Rotate[prGRup,Pi,{0,0,1}],2bet1,{0,1,0}],i2Pi/3,{0,0,1}],{i,3}];u1={prGRtilt,prGRup};add=Translate[prGR,{1.59,0,0.58}];u2=Translate[{u1,add},{0,0,diap}];u3=Rotate[Rotate[{u2},Pi,{0,0,1}],2bet1,{0,1,0}];u4=Table[Rotate[Rotate[{u2,u3},alf-bet1,{0,1,0}],i2Pi/5,{0,0,1}],{i,5}];u5=Rotate[u4,Pi,{0,1,0}];frame={u4,u5};Graphics3D[{u4},ImageSize300,BoxedFalse,SphericalRegionTrue,ViewPoint{0,0,100}]6
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Graphics3D[{frame},ImageSize300,BoxedFalse,SphericalRegionTrue,ViewPoint{0,0,100}]
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