TDK logo on Icosahedron
Sándor Kabai
The TDK logo seems to consists of a regular triangle, three squares attached to the triangle and a hexagonal frame. It fits into a larger triangle which can be placed on the faces of an icosahedron or a truncated icosahedron.
The TDK logo seems to consists of a regular triangle, three squares attached to the triangle and a hexagonal frame. It fits into a larger triangle which can be placed on the faces of an icosahedron or a truncated icosahedron.
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fi=GoldenRatio;alf=ArcTan[fi];bet=ArcTan[1/fi];bet1=ArcTan[1/fi^2];tv=Table[0.5/Sin[Pi/3]{Sin[2Pii/3+Pi],Cos[2Pii/3+Pi],0},{i,3}];x=Cos[Pi/6];y=Sin[Pi/6];u=0.5Sqrt[3]/3;u1=(x+1)Sqrt[3]/3;tri=Polygon[tv];vA={0.5,-0.5,0};vB={0.5,0.5,0};vC={-0.5,0.5,0};vD={-0.5,-0.5,0};vE={-Cos[Pi/6],-2u-y,0};vF={Cos[Pi/6],-2u-y,0};vG={x+0.5,-2u-y+0.5Sqrt[3],0};a=Tube[{vE,vF},0.04];b=Tube[{vF,vG},0.04];hex=Table[Rotate[{a,b},i2Pi/3,{0,0,1}],{i,3}];Graphics3D[{hex,tri},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->200]
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sv={vA,vB,vC,vD};square=Polygon[sv];ad4=Table[Rotate[Polygon[{vG,{0.5,u,0},{0.5,1+u,0}}],i2Pi/3,{0,0,1}],{i,3}];s4=Table[Rotate[Translate[square,{0,u+0.5,0}],i2Pi/3,{0,0,1}],{i,3}];Graphics3D[{ad4,Green,hex,Cyan,tri,Yellow,s4},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->200]
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(*Changethesequenceofverticesofthesquaretogettwotiangles*)sv={vA,vB,vD,vC};square=Polygon[sv];ad4=Table[Rotate[Polygon[{vG,{0.5,u,0},{0.5,1+u,0}}],i2Pi/3,{0,0,1}],{i,3}];s4=Table[Rotate[Translate[square,{0,u+0.5,0}],i2Pi/3,{0,0,1}],{i,3}];Graphics3D[{Red,hex,Green,tri,Yellow,s4},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->300]
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(*Thehexagonfitsintoatriangle*)tv1=Table[2.16{Sin[2Pii/3],Cos[2Pii/3],0},{i,4}];tri1=Line[tv1];i1={tri1,Cyan,ad4,Pink,hex,Cyan,s4,Pink,tri};i1={Pink,hex,Cyan,s4,Pink,tri};Graphics3D[{i1,tri1,hex},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->300]
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(*Placethelogoonanicosahedron*)i2=Translate[i1,{0,u1,0}];i3=Rotate[i2,-bet1,{1,0,0}];i4=Rotate[i3,Pi,{0,0,1}];i5=Table[Rotate[Rotate[Translate[{i3,i4},{0,0,(x+1)fi}],alf,{1,0,0}],i2Pi/5,{0,0,1}],{i,5}];Graphics3D[{i5},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->300]
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i6=Rotate[i5,Pi,{1,0,0}];ico=PolyhedronData["Icosahedron","Faces"];icon=Rotate[Scale[ico,1.99(x+1)],Pi/2,{0,0,1}];Graphics3D[{Yellow,icon,i5,i6},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->300]
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ticofit=Rotate[Scale[TruncatedPolyhedron[Icosahedron[],0.27],3.7],Pi/2,{0,0,1}];Graphics3D[{LightGreen,ticofit,i5,i6},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->300]