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(*Coordinatesinthecomplexplaneareused*)coor[z_]:={Re[z],Im[z]}(*choiceofthecolorfortheredpentagons*)redcol=RGBColor[200,0,0];(*choiceofthecolorforthebluepentagons*)bluecol=Blue;(*Risthelengthfromthecentertoaverticeinonepentagon*)R=1;(*rectangularunitcellfortheIce-raypacking*)(*complexcoordinateswithz0thecenterofthebluepentagon*)az=R*(1+Cos[Pi/5]);bz=3*R*I*Sin[2*Pi/5];z0=R*(Cos[Pi/5]*Exp[I*Pi/5]+Exp[2*I*Pi/5]);(*unitcelldependingontheslidingparameteru*)aunit[u_]:=az+2*u*R*I*Sin[Pi/5];bunit[u_]:=bz+2*u*R*(Cos[2*Pi/5]-1);(*aunit[u_]:=az+u*R*(Exp[I*Pi/5]-Exp[-I*Pi/5]);bunit[u_]:=bz-u*R*(1-Exp[8*I*Pi/5])+u*R*(Exp[2*I*Pi/5]-1);*)(*centersofthesixpentagonsaroundthebluepentagonatz0*)z1[u_]:=-u*R*(Exp[2*I*Pi/5]-1)z2[u_]:=z1[u]+aunit[u]z4[u_]:=z1[u]+aunit[u]+bunit[u]z5[u_]:=z1[u]+bunit[u]z3[u_]:=z0+aunit[u]z6[u_]:=z0-aunit[u](*verticesofaredpentagonsfromthecenter*)vertices=R*{1,Exp[2*I*Pi/5],Exp[4*I*Pi/5],Exp[6*I*Pi/5],Exp[8*I*Pi/5]};(*verticesofabluepentagonfromitscenter*)invertedvertices=R*{Exp[I*Pi/5],Exp[3*I*Pi/5],-1,Exp[7*I*Pi/5],Exp[9*I*Pi/5]};(*unitcellparametersandpackingfraction*)amodulus[u_]:=Abs[aunit[u]]bmodulus[u_]:=Abs[bunit[u]]angle[u_]:=Arg[bunit[u]]-Arg[aunit[u]]Airemaille[u_]:=amodulus[u]*bmodulus[u]*Sin[angle[u]]Airepentas=10*R^2*Sin[4*Pi/5]*Cos[Pi/5];PackingFraction[u_]:=Airepentas/Airemaille[u]
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(*rotationofthefiguresaroundthecenterofthebluepolygon*)(*rotationkeepsaunit[u]alwaysalongthex'xaxis*)RotFig[z_,u_]:=z*Exp[-I*Arg[aunit[u]]](*unitcellwithrotation*)aunitrot[u_]:=RotFig[aunit[u],u]bunitrot[u_]:=RotFig[bunit[u],u](*neighboursz1,toz6withrotation*)z1rot[u_]:=z0+RotFig[z1[u]-z0,u]z2rot[u_]:=z0+RotFig[z2[u]-z0,u]z3rot[u_]:=z0+RotFig[z3[u]-z0,u]z4rot[u_]:=z0+RotFig[z4[u]-z0,u]z5rot[u_]:=z0+RotFig[z5[u]-z0,u]z6rot[u_]:=z0+RotFig[z6[u]-z0,u](*pentagonswithrotation*)verticesrot[u_]:=Table[RotFig[vertices[[i]],u],{i,1,Length[vertices]}]invertedverticesrot[u_]:=Table[RotFig[invertedvertices[[i]],u],{i,1,Length[vertices]}](*directionfortheimageanalysis*)phirefimage[u_]:=-Pi/10-Arg[aunit[u]]
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(*rotationangleofthefiguredependingontheslidingparameteru*)(*closebutdifferentfromu*Pi/5*)Plot[{Arg[aunit[u]],u*Pi/5},{u,-0.5,0.5}]Pi/10/Degree//N;Arg[aunit[0.5]]/Degree//N;Plot[{phirefimage[u],-Pi/10-u*Pi/5},{u,-0.5,0.5}]
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(*anglesandbondsfunctions*)(*bondswithcolors*)BondPurple[u_]:=Abs[z1[u]-z0]BondYellow[u_]:=Abs[z2[u]-z0]BondGreen[u_]:=Abs[z3[u]-z0]BondCyan[u_]:=Abs[z4[u]-z0]BondRed[u_]:=Abs[z5[u]-z0](*angles*)AngleGreen[u_]:=-phirefimage[u]AngleCyan[u_]:=PlanarAngle[{coor[z3[u]],coor[z0],coor[z4[u]]}]-phirefimage[u]AngleRed[u_]:=PlanarAngle[{coor[z3[u]],coor[z0],coor[z5[u]]}]-phirefimage[u]AngleYellow[u_]:=PlanarAngle[{coor[z6[u]],coor[z0],coor[z2[u]]}]-phirefimage[u]AnglePurple[u_]:=PlanarAngle[{coor[z6[u]],coor[z0],coor[z1[u]]}]-phirefimage[u]
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(*versionwithrotationusingaunitrot[u]andbunitrot[u]*)Manipulate[Graphics[{Text["unit cell pentagonal ice-ray",{0,-1.5}],Style[Text["a",1.2*coor[aunitrot[u]]],Bold,12],Style[Text["b",1.2*coor[bunitrot[u]]],Bold,12],Style[Circle[{0,0},1],Dashed],Arrow[{{0,0},coor[aunitrot[u]]}],Arrow[{{0,0},coor[bunitrot[u]]}]},PlotRange{{-3,3},{-2,5}},ImageSize200],{{u,0,"sliding"},-0.5,0.5}]
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