function DEMOrubik(sparse)% Plot the two faithful representations for the% subgroup of the 2x2x2 Rubik's cube dealing with% 180-degree turns.if nargin == 0	sparse = 0;enddisp('|');disp('|  RUBIK REPRESENTATIONS');disp('|');disp('|  This shows two faithful representations of');disp('|  the 2x2x2 Rubik cube with half turns.');disp('|  The 3 turns t(blue), r(red), f(green)');disp('|  are represented by either plane reflections,');disp('|  (left) or line reflections (right).');disp('|');clf;subplot(1,2,1); rubik(-1,sparse); axis off; GAview([0 10]);subplot(1,2,2); rubik( 1,sparse); axis off; GAview([0 10]);b = axis;subplot(1,2,1); axis(b);subplot(1,2,2); axis(b);GAorbiter;function rubik(s,sparse)% draws faithful representation with sign s% sparse = 1: sparse draw% sparse = 0: draw allR = unit(((e2-e3)^e1)/I3);T = unit(((e3-e1)^e2)/I3);F = unit(((e1-e2)^e3)/I3);% choice of point affects figure severelye = unit(e1+0.3*(e2-2*e3));%e = unit(F+R);% e = unit(F);% e = unit(F -0.3*R+0.2*T);%clf;GAtext(1.1*e,'e');r = s*R*e/R; GAtext(1.1*r,'r');t = s*T*e/T; GAtext(1.1*t,'t');f = s*F*e/F; GAtext(1.1*f,'f');%tr = T*R*e/(T*R); GAtext(1.1*tr,'tr');rt = R*T*e/(R*T); GAtext(1.1*rt,'rt');rf = R*F*e/(R*F); GAtext(1.1*rf,'rf');fr = F*R*e/(F*R); GAtext(1.1*fr,'fr');ft = F*T*e/(F*T); GAtext(1.1*ft,'ft');tf = T*F*e/(T*F); GAtext(1.1*tf,'tf');%rfr = s*(R*F*R)*e/(R*F*R); GAtext(1.1*rfr,'rfr');rtr = s*(R*T*R)*e/(R*T*R); GAtext(1.1*rtr,'rtr');tft = s*(T*F*T)*e/(T*F*T); GAtext(1.1*tft,'tft');frt = s*(F*R*T)*e/(F*R*T); GAtext(1.1*frt,'frt');ftr = s*(F*T*R)*e/(F*T*R); GAtext(1.1*ftr,'ftr');trf = s*(T*R*F)*e/(T*R*F); GAtext(1.1*trf,'trf');tfr = s*(T*F*R)*e/(T*F*R); GAtext(1.1*tfr,'tfr');rtf = s*(R*T*F)*e/(R*T*F); GAtext(1.1*rtf,'rtf');rft = s*(R*F*T)*e/(R*F*T); GAtext(1.1*rft,'rft');%rfrt = (R*F*R*T)*e/(R*F*R*T); GAtext(1.1*rfrt,'rfrt');rftr = (R*F*T*R)*e/(R*F*T*R); GAtext(1.1*rftr,'rftr');rftf = (R*F*T*F)*e/(R*F*T*F); GAtext(1.1*rftf,'rftf');rtrf = (R*T*R*F)*e/(R*T*R*F); GAtext(1.1*rtrf,'rtrf');rtfr = (R*T*F*R)*e/(R*T*F*R); GAtext(1.1*rtfr,'rtfr');%% GAview([20 10]); axis off;if sparse==1   c2='w';   DrawPolygon({r,rtr,t},c2);DrawPolygon({tf,rftf,rtfr},c2);DrawPolygon({f,ftr,frt},c2);DrawPolygon({rfrt,rf,rftr},c2);DrawPolygon({rft,rfr,trf},c2);DrawPolygon({rtrf,ft,fr},c2);DrawPolygon({tft,tfr,rtf},c2);DrawPolygon({e,tr,rt},c2);elsec1 = 'w';c2 = 'y';c3 = 'w';if s== -1DrawPolygon({e,r,rt,rtr,tr,t},c2);DrawPolygon({rf,rfr,rfrt,trf,rftr,rft},c2);DrawPolygon({f,fr,frt,rtrf,ftr,ft},c2);DrawPolygon({tf,tfr,rtfr,rtf,rftf,tft},c2);%DrawPolygon({e,t,ft,f,tf,tft},c1);DrawPolygon({r,rftf,rtf,rf,rft,rt},c1);DrawPolygon({rfrt,rfr,rtfr,tfr,fr,frt},c1);DrawPolygon({rftr,trf,rtrf,ftr,tr,rtr},c1);%DrawPolygon({tf,tfr,fr,f},c3);DrawPolygon({tft,e,r,rftf},c3);DrawPolygon({rft,rftr,rtr,rt},c3);DrawPolygon({trf,rtrf,frt,rfrt},c3);DrawPolygon({rf,rtf,rtfr,rfr},c3);DrawPolygon({t,ft,ftr,tr},c3);elseDrawPolygon({r,rtr,t},c2);DrawPolygon({tf,rftf,rtfr},c2);DrawPolygon({f,ftr,frt},c2);DrawPolygon({rfrt,rf,rftr},c2);DrawPolygon({rft,rfr,trf},c2);DrawPolygon({rtrf,ft,fr},c2);DrawPolygon({tft,tfr,rtf},c2);DrawPolygon({e,tr,rt},c2);%DrawPolygon({fr,rtr,tf,rft},c3);DrawPolygon({f,rftr,tfr,rt},c3);DrawPolygon({t,rtfr,ftr,rf},c3);DrawPolygon({t,rtfr,ftr,rf},c3);DrawPolygon({e,frt,rftf,trf},c3);DrawPolygon({e,frt,rftf,trf},c3);DrawPolygon({tr,rfr,ft,rtf},c3);DrawPolygon({r,rfrt,tft,rtrf},c3);%DrawPolygon({r,fr,rtr},c1);DrawPolygon({r,fr,rtrf},c1);DrawPolygon({t,rtr,rtfr},c1);DrawPolygon({t,rfrt,rf},c1);DrawPolygon({tf,rtfr,rtr},c1);DrawPolygon({tf,rft,trf},c1);DrawPolygon({tf,trf,rftf},c1);DrawPolygon({rftf,ftr,rtfr},c1);DrawPolygon({rftf,frt,ftr},c1);DrawPolygon({f,frt,rt},c1);DrawPolygon({f,rftr,rf},c1);DrawPolygon({f,rf,ftr},c1);DrawPolygon({rfrt,r,t},c1);DrawPolygon({fr,ft,rft},c1);DrawPolygon({rfr,e,trf},c1);DrawPolygon({e,rt,frt},c1);DrawPolygon({e,rfr,tr},c1);DrawPolygon({rt,tr,tfr},c1);DrawPolygon({tr,rtf,tfr},c1);DrawPolygon({ft,rfr,rft},c1);DrawPolygon({tft,rfrt,rftr},c1);DrawPolygon({rtf,rtrf,ft},c1);DrawPolygon({tfr,tft,rftr},c1);DrawPolygon({tft,rtf,rtrf},c1);endendif s== -1   draw(pi*R/I3,'r');   draw(pi*F/I3,'g');   draw(pi*T/I3,'b');else   draw(1.2*R,'r');   draw(1.2*F,'g');   draw(1.2*T,'b');   draw(-1.2*R,'r');   draw(-1.2*F,'g');   draw(-1.2*T,'b');enddisp('|  END OF DEMO');disp('|');