1. Acute golden rhombohedron (prGR)
2. Obtuse golden rhombohedron (obGR)
3. Golden rhombic dodecahedron (Bilinski 1961 or RD2: 2 prGR + 2 obGR )
3. Rhombic icosahedron (RI, Fedorov 1887 : 5 prGR + 5 obGR )
4. Rhombic triacontahedron (RT, Kepler 1610: 10 prGR + 10 obGR)
(Notice the difference between 1961, 1887 and 1610)
2. Obtuse golden rhombohedron (obGR)
3. Golden rhombic dodecahedron (Bilinski 1961 or RD2: 2 prGR + 2 obGR )
3. Rhombic icosahedron (RI, Fedorov 1887 : 5 prGR + 5 obGR )
4. Rhombic triacontahedron (RT, Kepler 1610: 10 prGR + 10 obGR)
(Notice the difference between 1961, 1887 and 1610)
In[]:=
fi=GoldenRatio;alf=ArcTan[fi];bet=ArcTan[1/fi];bet1=ArcTan[1/fi^2];rtx=Cos[alf];rty=Sin[alf];p=N[rty/Cos[2Pi/20]];s=N[pSin[2Pi/20]];vert=Cylinder[{{0,0,-2},{0,0,3}},0.06];diap=N
3+
;diao=N6
5
3-
;cyl=Cylinder[{{-2.2,0,0},{1.6,0,0}},0.03];y=N[Sin[alf]];(*Bililnski*)vA={1/fi,0,-1};vB={0,1,-1};vC={-1/fi,0,-1};vD={0,-1,-1};b1=Polygon[{vA,vB,vC,vD}];vE={1/fi,1/fi,0};vF={1/fi,0,1};vG={1/fi,-1/fi,0};b2=Polygon[{vA,vE,vF,vG}];vI={0,-1,1};vH={0,-fi,0};b3=Polygon[{vA,vG,vH,vD}];b4=Polygon[{vG,vF,vI,vH}];b5=Rotate[{b3,b4},Pi,{1,0,0}];b6=Rotate[{b1,b2,b3,b4,b5},Pi,{0,1,0}];bil0={b1,b2,b3,b4,b5,b6};bil=Scale[bil0,rty];prGR=PolyhedronData["AcuteGoldenRhombohedron","Faces"];obGR=PolyhedronData["ObtuseGoldenRhombohedron","Faces"];ri=PolyhedronData["RhombicIcosahedron","Faces"];p1=Translate[prGR,{0,0,diap/2}];p2=Rotate[Rotate[p1,Pi,{0,0,1}],2bet1,{0,1,0}];p3=Table[Rotate[Rotate[{p1,p2},alf-bet1,{0,1,0}],i2Pi/5,{0,0,1}],{i,5}];p4=Rotate[p3,Pi,{0,1,0}];6
5
In[]:=
Manipulate(*Top3prGR*)p5top3=Table[Rotate[Rotate[p1,alf-bet1,{0,1,0}],i2Pi/5+6Pi/5+Pi,{0,0,1}],{i,3}];(*rock1*)top3=Translate[Rotate[p5top3,Pi+0.001,{0,1,0}],{2s,0,1.91+rock1}];(*RI*)rin=Translate[ri,{0,0,2diao}];rint=rin/.Polygon->Tube;rintfin=Rotate[rint,2bet,{0,1,0}];(*Bilinski*)bilfin=Rotate[Translate[Rotate[bil,alf,{0,1,0}],{0.42,0,0.9}],2bet,{0,1,0}];(*5obGR*)ob1=Rotate[Translate[obGR,{0,0,-diao/2}],-bet+bet1-Pi/2,{0,1,0}];(*rock2*)ob5=Table[Rotate[Translate[ob1,{-rock2+(-p-2s),0,1.344}],i2Pi/5,{0,0,1}],{i,5}];ob5fin=Rotate[Translate[{ob5},{0,0,-1}],2bet,{0,1,0}];(*5prGR*)p5top=Table[Rotate[Rotate[p1,alf-bet1,{0,1,0}],i2Pi/5,{0,0,1}],{i,5}];(*rock4*)p5fin=Rotate[Translate[{p5top},{0,0,-1-rock4}],2bet,{0,1,0}];(*rock3*)(*3obGR*)ob1up=Translate[Rotate[ob1,Pi,{0,0,1}],{2s,0,0.93+rock3}];ker1=Rotate[Translate[ob1,rock3+{2s+p,0,0.48}],2Pi/10,{0,0,1},{2s,0,0}];ker2=Rotate[Translate[ob1,rock3+{2s+p,0,0.48}],-2Pi/10,{0,0,1},{2s,0,0}];Graphics3D[{{Pink,ob5fin},{Cyan,p5fin},{Yellow,bilfin},{Red,rintfin},ker1,ker2,ob1up,{Green,vert},Green,top3},BoxedFalse,SphericalRegionTrue,ImageSize340,ViewPoint{10,-10,4},PlotRange3.6,ViewAngle0.07],{{rock2,0,"r2"},0,2},{{rock4,0,"r4"},0,2},{{rock3,0,"r3"},0,1.2},{{rock1,0,"r1"},0,1.8},TrackedSymbols{rock1,rock2,rock3,rock4},SaveDefinitions->True
Out[]=
