Filling space with RT, RH and RI
Sándor Kabai
Space filling structure is prepared with rhombic triacontahedron, rhombic hexecontahedron and rhombic icosahedron. Note: assemblies a5, a6, a7 and a8 are shown only once instead of 12 times.
Space filling structure is prepared with rhombic triacontahedron, rhombic hexecontahedron and rhombic icosahedron. Note: assemblies a5, a6, a7 and a8 are shown only once instead of 12 times.
In[]:=
Manipulateϕ=GoldenRatio;β=ArcTan[0.618];α=ArcTan[1.618];dodv=PolyhedronData["Dodecahedron","VertexCoordinates"];icov=PolyhedronData["Icosahedron","VertexCoordinates"];idv=PolyhedronData["Icosidodecahedron","VertexCoordinates"];rh={Rotate[Scale[PolyhedronData["RhombicHexecontahedron","Faces"],1/1.0514{1,1,1},{0,0,0}],Pi,{0,0,1}]};rh0={Yellow,Rotate[Scale[PolyhedronData["RhombicHexecontahedron","Faces"],1/1.0514{1,1,1},{0,0,0}],0Pi,{0,0,1}]};rt={Rotate[Scale[PolyhedronData["RhombicTriacontahedron","Faces"],1/1.0514{1,1,1},{0,0,0}],0Pi,{0,0,1}]};rt0={Rotate[Scale[PolyhedronData["RhombicTriacontahedron","Faces"],1/1.0514{1,1,1},{0,0,0}],Pi,{0,0,1}]};a0={Rotate[Map[Translate[rh,#]&,1.618^2icov],0×2Pi/10,{0,0,1}]};a1={RGBColor[0.5,0.6,0.9],Rotate[Map[Translate[rt,#]&,1.618^2idv],Pi,{0,0,1}]};a2={Yellow,Map[Translate[{rh},#]&,1.618^3dodv]};a3={Rotate[Map[Translate[rt,#]&,1.618^3idv],Pi,{0,0,1}]};ri={Rotate[Scale[PolyhedronData["RhombicIcosahedron","Faces"],1/1.0514{1,1,1},{0,0,0}],Pi,{0,0,1}]};ri0={Rotate[Scale[PolyhedronData["RhombicIcosahedron","Faces"],1/1.0514{1,1,1},{0,0,0}],0Pi,{0,0,1}]};rih=N1.0514;rhh=11.0514;riup=Translate[ri,{0,0,rih+rhh}];riup0=Translate[ri0,{0,0,rih+rhh}];ri5=Table[Rotate[Rotate[riup,2α,{0,1,0}],i2Pi/5+2Pi/10,{0,0,1}],{i,5}];ri51=Table[Rotate[Rotate[riup0,2β,{0,1,0}],i2Pi/5+0×2Pi/10,{0,0,1}],{i,5}];a4={Green,Translate[ri,{0,0,4.504}]};a5={Red,Translate[ri5,{0,0,1.618^4/1.0514}]};a6={RGBColor[0.3,1,0.9],Rotate[Map[Translate[{rh},#]&,1.618^4icov],2Pi/5,{0,0,1}]};a7={RGBColor[1,0.6,0.2],Translate[ri51,{0,0,1.618^4/1.0514}]};a8={Green,Translate[riup,{0,0,1.618^4/1.0514}]};Graphics3D[{If[a0s,a0,{}],If[a1s,a1,{}],If[a2s,a2,{}],If[a3s,a3,{}],If[a4s,a4,{}],If[a5s,a5,{}],If[a6s,a6,{}],If[a7s,a7,{}],If[a8s,a8,{}]},SphericalRegionTrue,BoxedFalse,ViewPoint{0,0,10},ViewAngle0.1,ImageSize400,PlotRange10],{{a0s,True,"a0-12RH"},{True,False}},{{a1s,False,"a1-30RT"},{True,False}},{{a2s,False,"a2-20RH"},{True,False}},{{a3s,False,"a3-30RT"},{True,False}},{{a4s,False,"a4-12RI"},{True,False}},{{a5s,False,"a5-12x5RI"},{True,False}},{{a6s,False,"a6-12RH"},{True,False}},{{a7s,False,"a7-12x5RI"},{True,False}},{{a8s,False,"a8-12RI"},{True,False}},ControlPlacementLeft,TrackedSymbolsManipulate
5
2
Out[]=
Graphics3D[{ri51,rh,riup}]
5
50-10
5
4.50401