Geometrical pattern on the windows of Rumbach synagogue in Budapest
Sándor Kabai
Geometrical pattern on the windows of Rumbach synagogue in Budapest is based mainly on octagonal symmetry. The central figure is fitted into a square. Thies is repeated eight times around a circle. Two pairs of parallel lines seem to represent the bracing of the window.
Geometrical pattern on the windows of Rumbach synagogue in Budapest is based mainly on octagonal symmetry. The central figure is fitted into a square. Thies is repeated eight times around a circle. Two pairs of parallel lines seem to represent the bracing of the window.
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fr=Table[0.5/Sin[Pi/4]{Sin[i2Pi/4+Pi/4],Cos[i2Pi/4+Pi/4],0},{i,5}];p4=Tube[fr];v0={-0.2,0.5,0};vA={-0.05,0.5,0};vB={0.1,0.1,0};vC={0.5,-0.05,0};vD={0.5,-0.2,0};abc=Tube[{v0,vA,vB,vC,vD},0.02];abc4=Table[Rotate[abc,i2Pi/4,{0,0,1}],{i,4}];abc8=Table[Rotate[abc,i2Pi/4+Pi/4,{0,0,1}],{i,4}];u1={abc4,abc8};u2=Table[Rotate[Translate[u1,{1,1,0}],i2Pi/4,{0,0,1}],{i,4}];u3=Table[Rotate[Translate[u1,{0,1.41,0}],i2Pi/4,{0,0,1}],{i,4}];fv=Table[1.96{Sin[i2Pi/16+2Pi/32],Cos[i2Pi/16+2Pi/32],0},{i,17}];frame=Tube[fv,0.02];v1=Tube[{{-0.5,1.86,0},{-0.5,-1.86,0}},0.022];v2=Translate[v1,{1,0,0}];v3=Rotate[{v1,v2},Pi/2,{0,0,1}];vE={-0.5,0.3,0};vF={-0.2,0.5,0};e1=Tube[{vE,vF}];f8=Table[0.22{Sin[i2Pi/8+Pi/8]-3.2,Cos[i2Pi/8+Pi/8]+1.36,0},{i,9}];p8a=Tube[f8,0.02];p8b=Translate[p8a,{0,-0.6,0}];p8ab=Table[Rotate[{p8a,p8b},i2Pi/4,{0,0,1}],{i,4}];ar=Table[Rotate[Tube[{{-0.2,0.5,0},{0,0.74,0},{0.2,0.5,0}}],i2Pi/4,{0,0,1}],{i,4}];co1=Tube[{{-0.9,1.7,0},{-0.76,1.5,0},{-0.6,1.5,0},{-0.5,1.6,0}},0.02];co2=Rotate[co1,Pi,{0,1,0}];co=Table[Rotate[{Red,co1,co2},i2Pi/4,{0,0,1}],{i,4}];Graphics3D[{co,Cyan,ar,p8ab,Purple,v1,v2,v3,Pink,frame,u1,Cyan,u2,Yellow,u3},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->400]
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Now the process of constrution is shown step by step below.
(*Thisistheunit,eightofwhichcreatethecentralfigure*)Graphics3D[{p4,abc},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->300]
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Graphics3D[{Pink,p4,Green,abc4},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->300]
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Graphics3D[{v1,u2,Pink,p4,Green,abc4,Yellow,abc8},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->300]
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Graphics3D[{v1,p4,Yellow,u2,Pink,u3,Green,abc4,Yellow,abc8},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->300]
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Graphics3D[{Pink,frame,Purple,v1,v2,v3,Yellow,u2,Pink,u3,Green,abc4,Yellow,abc8},Boxed->False,SphericalRegion->True,ViewPoint->{0,0,100},ImageSize->300]
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