Five rhombi are placed at each five - fold vertex of a rhombic triacontahedron (RT). As the rhombi grow (as if they were five petals of a flower), they finally meet to form a rhombic hexecontahedron .
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Manipulate[ϕ=GoldenRatio;β=ArcTan[1/ϕ];vA={1/ϕ,0,0};vB={0,1,0};vC={-1/ϕ,0,0};vD={0,-1,0};r1=Polygon[{vA,vB,vC,vD}];x=y/ϕ;vE={x,1+y,0};vF={0,1+2y,0};vG={-x,1+y,0};r2={RGBColor[1,0.4,0],Polygon[{vB,vE,vF,vG}]};r3=Rotate[r2,Pi,{0,0,1}];p1=Translate[{r1,r2,r3},{0,0,ϕ}];p2=Translate[{r1,r2,r3},{0,0,-ϕ}];p3=Rotate[Rotate[{p1,p2},Pi/2,{1,0,0}],Pi/2,{0,1,0}];p4=Rotate[Rotate[{p1,p2},Pi/2,{0,0,1}],Pi/2,{0,1,0}];rt1=Rotate[{p1,p2,p3,p4},β,{1,0,0}];rt=Table[Rotate[rt1,i2Pi/5,{0,0,1}],{i,5}];Graphics3D[{rt},BoxedFalse,ImageSize400,ViewAngle0.1,PlotRange4.4,ViewPoint{0,0,10}],{{y,0,"grow"},0,ϕ},TrackedSymbolsManipulate,SaveDefinitionsTrue]
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