{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" -1 35 "" 0 1 104 64 92 1 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 " Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "restart:with(geom3d) :with(linalg):with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, th e name changecoords has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 43 "Warning, the name polar has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 45 "Warning, the name inverse has been redefined\n" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace hav e been redefined and unprotected\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 127 "Programme de vision en relief d'un poly\350dre R. ferreol 2005 ;\n regarder avec lunettes \340 verre gauche rouge, et verre droit ble u." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 120 "L'oeil est plac\351 en A=( a,b,c), regarde un objet plac\351 en M=(x,y,z) a travers le plan passa nt par O et orthogonal \340 (OA)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 196 "X:=(1-t)*a+t*x:\nY:=(1-t)*b+t*y:\nZ:=(1-t)*c+t*z:\nt :=solve(a*X+b*Y+c*Z,t):r:=sqrt(a^2+b^2+c^2):s:=sqrt(a^2+b^2):A:=matrix (3,3,[a/r,-b/s,-a*c/r/s,b/r,a/s,-b*c/r/s,c/r,0,(a^2+b^2)/r/s]):B:=inve rse(A):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "C:=simplify(mult iply(B,matrix(3,1,[X,Y,Z]))):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 235 "le suffixe r (comme rouge), concerne l'oeil droit (comme il regarde p ar le verre bleu, il ne voit que le trac\351 rouge)\nle suffixe b (com me bleu), concerne l'oeil gauche (comme il regarde par le verre rouge, il ne voit que le trac\351 bleu)" }{TEXT 256 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 243 "xr:=subs([a=ar,b=br,c=cr],s*C[2,1]):xr:=una pply(xr,[x,y,z]):\nxb:=subs([a=ab,b=bb,c=cb],s*C[2,1]):xb:=unapply(xb, [x,y,z]):\nyr:=subs([a=ar,b=br,c=cr],s*C[3,1]):yr:=unapply(yr,[x,y,z]) :\nyb:=subs([a=ab,b=bb,c=cb],s*C[3,1]):yb:=unapply(yb,[x,y,z]):" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 156 "l'oeil droit a pour longitude the ta+eps et pour latitude lambda ; l'oeil gauche a pour longitude theta- eps et pour latitude lambda ; la distance \340 O est d." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 212 "d:=10:theta:=Pi/3:lambda:=Pi/5:eps :=0.05:\nar:=d*cos(theta+eps)*cos(lambda):br:=d*sin(theta+eps)*cos(lam bda):cr:=d*sin(lambda):\nab:=d*cos(theta-eps)*cos(lambda):bb:=d*sin(th eta-eps)*cos(lambda):cb:=d*sin(lambda):\n" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 308 "projb:=proc(M)\n[xb(seq(M[i],i=1..3)),yb(seq(M[i], i=1..3))]\nend:\nprojfaceb:=proc(face)\nmap(projb,face)\nend:\nprojpol yb:=proc(poly)\nmap(projfaceb,poly)\nend:\nprojr:=proc(M)\n[xr(seq(M[i ],i=1..3)),yr(seq(M[i],i=1..3))]\nend:\nprojfacer:=proc(face)\nmap(pro jr,face)\nend:\nprojpolyr:=proc(poly)\nmap(projfacer,poly)\nend:\n" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "hexahedron(p,point(o,0,0,0 ),1):cube:=evalf(faces(p)):\ntetrahedron(pp,point(o,0,0,0),1):poly:=ev alf(faces(pp)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 261 "display (plot(projpolyr(poly),color=red),\nplot(projpolyb(poly),color=COLOR(RG B, 0/256, 256/256, 256/256),thickness=2),\nplot(projpolyr(cube),color =red),\nplot(projpolyb(cube),color=COLOR(RGB, 0/256, 256/256, 256/256 ),thickness=2),\naxes=none,scaling=constrained);" }}{PARA 13 "" 1 "" {GLPLOT2D 398 395 395 {PLOTDATA 2 "6:-%'CURVESG6$7%7$$!3Uold'e1OC#!#<$ \"3V1X2*R6yA*!#>7$$!3AZI>wW&Q'fF*$!3E8t.7'pYX#F*7$$\"3DE)HW'))H-iF*$!3 ))*)R2T,(G!\\F*-%'COLOURG6&%$RGBG$\"*++++\"!\")$\"\"!F@F?-F$6$7%F'7$$ \"3Y4#\\QtC%p>F*$\"3Eu5$z*33ksF*F.F8-F$6$7%F'F3FDF8-F$6$7%F.FDF3F8-F$6 %7%7$$!3?H?gWdPS:F*$!3qQ_-8uK(*=F-7$$!3a4]0\"y\\K;'F*$!3`i4%*GBQFGF*7$ $\"3=:SfzT0JjF*$!3+a$)*=N-Z]%F*-%&COLORG6&F;F@\"\"\"F^o-%*THICKNESSG6# \"\"#-F$6%7%FR7$$\"3i:X`gmLZ8F*$\"3ynX`R&)\\\\tF*FWF[oF_o-F$6%7%FRFfnF foF[oF_o-F$6%7%FWFfoFfnF[oF_o-F$6$7&F'7$$!3iJ#zdZTUP'F*$\"3V_&3$p%*yQ] F*F.7$$!3i=\"z^(>z'3#F*$!3]SOD\"\\\")pp(F*F8-F$6$7&7$$\"33!='*\\D#QZmF *$\"3U3d$Re.gt#F*F37$$\"3An4c)eav%=F*$!3)4V4Xou))f(F-FDF8-F$6$7&F'FipF 3FaqF8-F$6$7&FdpFDFfqF.F8-F$6$7&F'FaqFDFdpF8-F$6$7&F.FfqF3FipF8-F$6%7& FR7$$!3?k%=m)y6!f'F*$\"3E@X@;E.*o%F*FW7$$!3PU$[[$H_K9F*$!3s;5:qb<9yF*F [oF_o-F$6%7&7$$\"3mp_Z[SL#y'F*$\"3x;\"**>Q'Q6JF*Ffn7$$\"3kZGd1<4k7F*$ \"3[_Vj.+-d:F-FfoF[oF_o-F$6%7&FRF_sFfnFgsF[oF_o-F$6%7&FjrFfoF\\tFWF[oF _o-F$6%7&FRFgsFfoFjrF[oF_o-F$6%7&FWF\\tFfnF_sF[oF_o-%(SCALINGG6#%,CONS TRAINEDG-%+AXESLABELSG6%Q!6\"Fdu-%%FONTG6#%(DEFAULTG-%*AXESSTYLEG6#%%N ONEG-%%VIEWG6$FiuFiu" 1 2 0 1 10 0 2 9 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" "Cu rve 13" "Curve 14" "Curve 15" "Curve 16" "Curve 17" "Curve 18" "Curve \+ 19" "Curve 20" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "GreatStel latedDodecahedron(p,point(o,0,0,0),1):poly:=evalf(faces(p)):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "polygonplot3d(poly,color=bla ck,style=wireframe,scaling=constrained);" }}{PARA 13 "" 1 "" {GLPLOT3D 458 379 379 {PLOTDATA 3 "6&-%)POLYGONSG6.7&7%$\"+5y1rq!#5F($ !+5y1rqF*7%$\"+iN@99!\"*$\"\"!F2F17%F(F(F(7%F1F.F17&7%F+F(F+7%$!+iN@99 F0F1F17%F+F+F+7%F1F1F87&F37%F1F1F.7%F+F(F(F47&F3F=7%F(F+F(F-7&7%F(F+F+ 7%F1F8F1F:F;7&FBFCF@F-7&7%F+F+F(F=F@FC7&F'F;FBF-7&F6F7F>F47&FFF=F>F77& FFF7F:FC7&F'F;F6F4-%(SCALINGG6#%,CONSTRAINEDG-%&STYLEG6#%%LINEG-%'COLO URG6&%$RGBGF2F2F2" 1 6 0 1 10 0 2 6 1 1 1 1.000000 51.000000 129.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "RhombicDodecahedron(p,point(o,0,0,0),1):poly:=evalf(faces(p)):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "TruncatedOctahedron(p,point( o,0,0,0),1):poly:=evalf(faces(p)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 180 "display(plot(projpolyr(poly),color=COLOR(RGB, 256/2 56, 0/256, 0/256)),\nplot(projpolyb(poly),color=COLOR(RGB, 0/256, 256 /256, 256/256),thickness=2),axes=none,scaling=constrained);" }}{PARA 13 "" 1 "" {GLPLOT2D 258 324 324 {PLOTDATA 2 "6>-%'CURVESG6$7&7$$!3gLw Rcj)f>#!#<$!3S$)>X.lGn&*F*7$$!3/_Up_pM_5!#;$!3==mY*oZ\"[NF*7$$!3R-;JHz L.CF*$\"3SMoc!)**\\\\V!#>7$$\"3\"))4IV0]+K'F*$!3!3Dju(Q7wkF*-%&COLORG6 &%$RGBG\"\"\"\"\"!FC-F$6$7&7$$\"3)y&e)e\"zX_wF*$!3c,k)Gq$GadF*7$$\"3Ix J2-*R)*Q*F*$\"3Q#pSABFf;$F*7$$\"3iN#oRJ$o*)=F*$!3$443e*3!*>MF87$$FCFC$ !3%3[AR\"pxX&)F*F>-F$6$7&F37$FW$\"30An6!eK&45F07$$\"3?w'RokQ6L)F*$\"3S #y-F$6$7&F3Fgn7$$!3)*)Gd]$zDrzF*$\"3i/e0Eh+%*fF*F-F>-F$6$ 7&7$$!3%e>f,s]xM(F*$!3qa*=1g-Z=$F*7$$!3)4\">V#Ha)y^F*$\"3*RP^CDYnI&F*F QFVF>-F$6$7&FjoF_pFboF-F>-F$6$7&7$$\"3'yk(f8!H7/#F*$\"3GKdZ!)G0$*))F*F gnFboF_pF>-F$6$7&F'FVFjoF-F>-F$6$7&FGFLFjnF9F>-F$6$7&FjpFgnFjnFLF>-F$6 $7&FjpFLFQF_pF>-F$6$7&F'FVFGF9F>-F$6%7&7$$!3'*R*=*)4o$y8F*$!39\"yp'f*o '*o*F*7$$!3SD#445#**p**F*$!3KNg%H()32>%F*7$$!3Wbxc>Gx3:F*$!33fs=Ej#G;( F87$$\"3&Gb\")R!e3QtF*$!3Cnm.8)H:.'F*-F?6&FAFCFBFB-%*THICKNESSG6#\"\"# -F$6%7&7$$\"3/&y/kfK6w(F*$!3C\\'pp`E%e_F*7$$\"341qeN$eds)F*$\"3Y5v=Ptr nOF*7$$\"33oiI'fq@=\"F*$\"3N96S%*zH7cF8FVFesFgs-F$6%7&F[sFgn7$$\"3\"Q- =fT(pV%)F*$\"3S\\B*y-0@2%F*F`sFesFgs-F$6%7&F[sFgn7$$!3C(zjH$zI8#)F*$\" 3S?@/H/zkbF*FfrFesFgs-F$6%7&7$$!3g>.5,a0mvF*$!3?\\kR^%[)[OF*7$$!3ks))e V0a)3'F*$\"3N@*GtvnW+&F*FhtFVFesFgs-F$6%7&F`vFevFhuFfrFesFgs-F$6%7&7$$ \"3!f'ee/\">oF\"F*$\"3UFIQ%f)zv*)F*FgnFhuFevFesFgs-F$6%7&FarFVF`vFfrFe sFgs-F$6%7&F^tFctF`uF`sFesFgs-F$6%7&F`wFgnF`uFctFesFgs-F$6%7&F`wFctFht FevFesFgs-F$6%7&FarFVF^tF`sFesFgs-%(SCALINGG6#%,CONSTRAINEDG-%+AXESLAB ELSG6%Q!6\"F[y-%%FONTG6#%(DEFAULTG-%*AXESSTYLEG6#%%NONEG-%%VIEWG6$F`yF `y" 1 2 0 1 10 0 2 9 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curv e 15" "Curve 16" "Curve 17" "Curve 18" "Curve 19" "Curve 20" "Curve 21 " "Curve 22" "Curve 23" "Curve 24" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "#Trunca tedTetrahedron(gon, o, r)" }}{PARA 0 "" 0 "" {TEXT -1 25 " Truncat edOctahedron(" }{TEXT 35 3 "gon" }{TEXT -1 2 ", " }{TEXT 35 1 "o" } {TEXT -1 2 ", " }{TEXT 35 1 "r" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 25 " TruncatedHexahedron(" }{TEXT 35 3 "gon" }{TEXT -1 2 ", " }{TEXT 35 1 "o" }{TEXT -1 2 ", " }{TEXT 35 1 "r" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 26 " TruncatedIcosahedron(" }{TEXT 35 3 "gon" }{TEXT -1 2 ", " }{TEXT 35 1 "o" }{TEXT -1 2 ", " }{TEXT 35 1 "r" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 27 " TruncatedDodec ahedron(" }{TEXT 35 3 "gon" }{TEXT -1 2 ", " }{TEXT 35 1 "o" }{TEXT -1 2 ", " }{TEXT 35 1 "r" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 30 " SmallRhombicuboctahedron(" }{TEXT 35 3 "gon" }{TEXT -1 2 ", \+ " }{TEXT 35 1 "o" }{TEXT -1 2 ", " }{TEXT 35 1 "r" }{TEXT -1 1 ")" }} {PARA 0 "" 0 "" {TEXT -1 34 " SmallRhombiicosidodecahedron(" } {TEXT 35 3 "gon" }{TEXT -1 2 ", " }{TEXT 35 1 "o" }{TEXT -1 2 ", " } {TEXT 35 1 "r" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 30 " Gre atRhombicuboctahedron(" }{TEXT 35 3 "gon" }{TEXT -1 2 ", " }{TEXT 35 1 "o" }{TEXT -1 2 ", " }{TEXT 35 1 "r" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 28 " TruncatedCuboctahedron(" }{TEXT 35 3 "gon" } {TEXT -1 2 ", " }{TEXT 35 1 "o" }{TEXT -1 2 ", " }{TEXT 35 1 "r" } {TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 34 " GreatRhombiicosidod ecahedron(" }{TEXT 35 3 "gon" }{TEXT -1 2 ", " }{TEXT 35 1 "o" }{TEXT -1 2 ", " }{TEXT 35 1 "r" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 32 " TruncatedIcosidodecahedron(" }{TEXT 35 3 "gon" }{TEXT -1 2 ", " }{TEXT 35 1 "o" }{TEXT -1 2 ", " }{TEXT 35 1 "r" }{TEXT -1 1 ")" }} {PARA 0 "" 0 "" {TEXT -1 14 " SnubCube(" }{TEXT 35 3 "gon" }{TEXT -1 2 ", " }{TEXT 35 1 "o" }{TEXT -1 2 ", " }{TEXT 35 1 "r" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 22 " SnubDodecahedron(" }{TEXT 35 3 "gon" }{TEXT -1 2 ", " }{TEXT 35 1 "o" }{TEXT -1 2 ", " }{TEXT 35 1 "r" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 19 " cuboctahe dron(" }{TEXT 35 3 "gon" }{TEXT -1 2 ", " }{TEXT 35 1 "o" }{TEXT -1 2 ", " }{TEXT 35 1 "r" }{TEXT -1 1 ")" }}{PARA 0 "" 0 "" {TEXT -1 23 " \+ icosidodecahedron(" }{TEXT 35 3 "gon" }{TEXT -1 2 ", " }{TEXT 35 1 "o" }{TEXT -1 2 ", " }{TEXT 35 1 "r" }{TEXT -1 441 ") duality \+ faces HexakisIcosahedron HexakisOc tahedron \nPentagonalHexacontahedron PentagonalIcositetrahed ron PentakisDodecahedron radius RhombicDodecahedro n \nRhombicTriacontahedron schlafli Tetra kisHexahedron TrapezoidalHexecontahedron TrapezoidalIcositetrahedron \nTriakisIcosahedron TriakisOctahedron TriakisTetrahe dron ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 46 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }