Shape of a lamp in Dohány synagogue in Budapest
Sándor Kabai
The lamp fixture is a stellated truncated cube. The truncation is made in such a way that a hexagon is formed on the cube surface. The basic shape has two square, four hexagonal and eight triangular faces.
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d=Table[{Sin[i2Pi/3],Cos[i2Pi/3],0},{i,0,3}];​​d1={Tube[d,0.05]};​​d2=Rotate[d1,Pi,{0,0,1}];​​d12={Yellow,d1,d2};​​Graphics3D[{d12},BoxedFalse,SphericalRegionTrue,ViewPoint{0,0,100},ImageSize->100]
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Needs["PolyhedronOperations`"];​​cub=PolyhedronData["Cube","Faces"];​​square=Polygon[{{0,-0.5,0.5},{0.5,0,0.5},{0,0.5,0.5},{-0.5,0,0.5}}];​​cubt=cub/.Polygon->Tube;​​d12n=Translate[Scale[d12,0.35],{0,0,0.5}];​​Graphics3D[{d12n,Red,square,Cyan,cubt},ImageSize300,Boxed->False,SphericalRegion->True]
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tri=Polygon[{{0,-0.5,0.5},{0.5,0,0.5},{0.5,-0.5,0.25}}];​​hex=Polygon[{{0,-0.5,0.5},{-0.5,-0.5,0.25},{-0.5,-0.5,-0.25},{0,-0.5,-0.5},{0.5,-0.5,-0.25},{0.5,-0.5,0.25}}];​​cubt=cub/.Polygon->Tube;​​Graphics3D[{d12n,Cyan,tri,Pink,square,Green,hex,White,cubt},ImageSize300,Boxed->False,SphericalRegion->True]
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hex4=Table[Rotate[hex,i2Pi/4,{0,0,1}],{i,4}];​​tri4=Table[Rotate[tri,i2Pi/4,{0,0,1}],{i,4}];​​squaredown=Table[Rotate[square,iPi,{0,1,0}],{i,2}];​​tri4down=Rotate[{d12n,tri4},Pi,{0,1,0}];​​Graphics3D[{d12n,hex4,tri4,square,squaredown,tri4down},ImageSize300,Boxed->False,SphericalRegion->True]
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​​full={Cyan,hex4,Pink};​​fullst=Stellate[full,2.6];​​trist=Stellate[{tri4,tri4down},1.8];​​ready={trist,fullst};​​Graphics3D[{trist,d12n,ready,Pink,square,squaredown},ImageSize400,Boxed->False,SphericalRegion->True]
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p1=0.4;​​ee=Normal[ready]/.p:Polygon[__](p/.pts:{{_?NumericQ,_,_},__}Module[{cent,innervtx},cent=Mean[pts];​​innervtx={1-p1,p1}.{#,cent}&/@pts;​​Join[pts,pts[[{1}]],innervtx,innervtx[[{1}]]]])//#&;​​​​Graphics3D[{tri4down,tri4,ee,d12n,full,Red,square,squaredown},ImageSize400,Boxed->False,SphericalRegion->True]
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