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\deflang1031\pard\ri4\plain\f4\fs20\cf0\b ________________________________________________________________________________
\par 
\par \plain\f4\fs20\cf0 Inhalt....: Archimedischer K\'f6rper: Abgestumpftes Ikosidodekaeder
\par Kategorie.: Grafik
\par Mathematik: Grafik, Geometrie R^3 
\par MuPAD.....: 3.1.1
\par Datum.....: 2005-06-24
\par Autoren...: Tobias Fankh\'e4nel <fank1@gmx.de>
\par Autoren...: Andreas Sorgatz <sorgatz@sciface.com>
\par Funktionen: SurfaceSet, Scaling, Constrained, Header, Footer, BackgroundStyle 
\par Funktionen: Axes, Width, Height, BorderWidth, FooterFont, FooterAlignment 
\par Funktionen: plot, plot::Rotate3d, Frames, Margin
\par \plain\f4\fs20\cf0\b ________________________________________________________________________________
\par \plain\f3\fs36\cf0 
\par Archimedischer K\'f6rper
\par \plain\f6\fs24\cf0 Abgestumpftes Ikosidodekaeder oder gro\'dfes Rhombenikosidodekaeder (4,6,10)
\par 
\par \plain\f6\fs24\cf0\ul Definition\plain\f6\fs24\cf0 : Ein Polyeder hei\'dft halbregul\'e4r oder semiregul\'e4r, wenn alle seine Oberfl\'e4chen aus 
\par regelm\'e4\'dfigen Vielecken (eventuell unterschiedlicher Eckenzahl) bestehen, und jede Ecke des 
\par Polyeders durch eine seiner Symmetrieoperationen auf jede andere Ecke abgebildet werden 
\par kann. Es mu\'df sich also um ein uniformes Polyeder handeln.
\par 
\par Bereits Platon soll neben den nach ihm benannten regul\'e4ren Polyedern das Kuboktaeder ge-
\par kannt haben. Seit Archimedes, dessen Arbeit dar\'fcber jedoch nicht erhalten geblieben ist, wei\'df
\par man, da\'df es neben den Platonischen K\'f6rpern (und unendlich vielen Prismen und Antiprismen)
\par noch genau dreizehn halbregul\'e4re konvexe Polyeder gibt, die \'fcblicherweise als Archimedische
\par K\'f6rper bezeichnet werden. (\plain\f6\fs20\cf0 Quelle: http://www.mathe.tu-freiberg.de/~hebisch/cafe/archimedische.html\plain\f6\fs24\cf0 )
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs22\cf2 {\pntext\f1\'b7\tab}p0  := 0,\tab \tab  0,\tab \tab \tab  0.655694:
\par \pard\li600\ri1\fi-300\plain\f4\fs22\cf2 p1  := 0.1709448,\tab  0,\tab \tab \tab  0.6330181:
\par p2  :=-0.00300786,\tab  0.17091815,\tab  0.6330181:
\par p3  :=-0.1437384,\tab -0.0925275,\tab  0.6330181:
\par p4  := 0.16793725,\tab  0.17091815,\tab  0.61034285:
\par p5  := 0.3038009,\tab -0.0925275,\tab  0.57365295:
\par p6  :=-0.14975415,\tab  0.24930945,\tab  0.58766695:
\par p7  :=-0.2053675,\tab -0.2422407,\tab  0.57365295:
\par p8  :=-0.290485,\tab -0.01413698,\tab  0.58766695:
\par p9  := 0.29778515,\tab  0.24930945,\tab  0.5283018:
\par p10 := 0.3478215,\tab -0.2422407,\tab  0.5002738:
\par p11 := 0.43364945,\tab -0.01413698,\tab  0.49161255:
\par p12 :=-0.21625045,\tab  0.37614785,\tab  0.49161255:
\par p13 :=-0.2934932,\tab  0.1567813,\tab  0.5649917:
\par p14 :=-0.3521141,\tab -0.16385005,\tab  0.5283018:
\par p15 :=-0.1613469,\tab -0.3919539,\tab  0.5002738:
\par p16 := 0.3369392,\tab  0.37614785,\tab  0.41823275:
\par p17 := 0.43064125,\tab  0.1567813,\tab  0.46893665:
\par p18 := 0.47767005,\tab -0.16385005,\tab  0.41823275:
\par p19 := 0.2861924,\tab -0.3919539,\tab  0.440908:
\par p20 :=-0.35998885,\tab  0.28362035,\tab  0.46893665:
\par p21 :=-0.1770964,\tab  0.5029869,\tab  0.38154285:
\par p22 :=-0.4548401,\tab -0.23517195,\tab  0.4095715:
\par p23 :=-0.0284908,\tab -0.4844814,\tab  0.440908:
\par p24 :=-0.2640729,\tab -0.4632758,\tab  0.38154285:
\par p25 := 0.4697953,\tab  0.28362035,\tab  0.3588676:
\par p26 := 0.27044355,\tab  0.5029869,\tab  0.3221777:
\par p27 := 0.54588885,\tab -0.23517195,\tab  0.2768272:
\par p28 := 0.142454,\tab -0.4844814,\tab  0.41823275:
\par p29 := 0.35441185,\tab -0.4632758,\tab  0.29950245:
\par p30 :=-0.4645732,\tab  0.31793125,\tab  0.33619235:
\par p31 :=-0.04724798,\tab  0.58137755,\tab  0.29950245:
\par p32 :=-0.28168075,\tab  0.5372978,\tab  0.24879855:
\par p33 :=-0.55942445,\tab -0.20086105,\tab  0.2768272:
\par p34 :=-0.41081885,\tab -0.38488515,\tab  0.33619235:
\par p35 :=-0.1312168,\tab -0.55580395,\tab  0.3221777:
\par p36 := 0.53615575,\tab  0.31793125,\tab  0.2034474:
\par p37 := 0.12369695,\tab  0.58137755,\tab  0.2768272:
\par p38 := 0.33680335,\tab  0.5372978,\tab  0.16675815:
\par p39 := 0.6122493,\tab -0.20086105,\tab  0.121407:
\par p40 := 0.4842604,\tab -0.38488515,\tab  0.21746205:
\par p41 := 0.21067345,\tab -0.55580395,\tab  0.2768272:
\par p42 :=-0.5672992,\tab  0.24660935,\tab  0.21746205:
\par p43 :=-0.4254198,\tab  0.4447703,\tab  0.2261233:
\par p44 :=-0.15183285,\tab  0.6156891,\tab  0.16675815:
\par p45 :=-0.51540385,\tab -0.35057425,\tab  0.2034474:
\par p46 :=-0.6259201,\tab -0.074022,\tab \tab  0.18077215:
\par p47 :=-0.06299735,\tab -0.62712585,\tab  0.18077215:
\par p48 := 0.60437455,\tab  0.24660935,\tab  0.06204165:
\par p49 := 0.46965945,\tab  0.4447703,\tab  0.10739235:
\par p50 := 0.1900574,\tab  0.6156891,\tab  0.121407:
\par p51 := 0.5506202,\tab -0.35057425,\tab  0.06204165:
\par p52 := 0.651404,\tab -0.074022,\tab \tab  0.01133776:
\par p53 := 0.10794745,\tab -0.62712585,\tab  0.15809625:
\par p54 :=-0.52814515,\tab  0.3734484,\tab  0.10739235:
\par p55 :=-0.6289283,\tab  0.09689615,\tab  0.15809625:
\par p56 :=-0.0854724,\tab  0.65,\tab \tab  0.01133776:
\par p57 :=-0.5378789,\tab -0.3734484,\tab  0.0340132:
\par p58 :=-0.64839515,\tab -0.09689615,\tab  0.01133776:
\par p59 :=-0.0854724,\tab -0.65,\tab \tab  0.01133776:
\par p60 := 0.5378789,\tab  0.3734484,\tab -0.0340132:
\par p61 := 0.64839515,\tab  0.09689615,\tab -0.01133776:
\par p62 := 0.0854724,\tab  0.65,\tab \tab -0.01133776:
\par p63 := 0.52814515,\tab -0.3734484,\tab -0.10739235:
\par p64 := 0.6289283,\tab -0.09689615,\tab -0.15809625:
\par p65 := 0.0854724,\tab -0.65,\tab \tab -0.01133776:
\par p66 :=-0.5506202,\tab  0.35057425,\tab -0.06204165:
\par p67 :=-0.651404,\tab  0.074022,\tab \tab -0.01133776:
\par p68 :=-0.10794745,\tab  0.62712585,\tab -0.15809625:
\par p69 :=-0.46965945,\tab -0.4447703,\tab -0.10739235:
\par p70 :=-0.60437455,\tab -0.24660935,\tab -0.06204165:
\par p71 :=-0.1900574,\tab -0.6156891,\tab -0.121407:
\par p72 := 0.51540385,\tab  0.35057425,\tab -0.2034474:
\par p73 := 0.6259201,\tab  0.074022,\tab \tab -0.18077215:
\par p74 := 0.06299735,\tab  0.62712585,\tab -0.18077215:
\par p75 := 0.4254198,\tab -0.4447703,\tab -0.2261233:
\par p76 := 0.5672992,\tab -0.24660935,\tab -0.21746205:
\par p77 := 0.15183285,\tab -0.6156891,\tab -0.16675815:
\par p78 :=-0.4842604,\tab  0.38488515,\tab -0.21746205:
\par p79 :=-0.6122493,\tab  0.20086105,\tab -0.121407:
\par p80 :=-0.21067345,\tab  0.55580395,\tab -0.2768272:
\par p81 :=-0.53615575,\tab -0.31793125,\tab -0.2034474:
\par p82 :=-0.33680335,\tab -0.5372978,\tab -0.16675815:
\par p83 :=-0.12369695,\tab -0.58137755,\tab -0.2768272:
\par p84 := 0.41081885,\tab  0.38488515,\tab -0.33619235:
\par p85 := 0.55942445,\tab  0.20086105,\tab -0.2768272:
\par p86 := 0.1312168,\tab  0.55580395,\tab -0.3221777:
\par p87 := 0.4645732,\tab -0.31793125,\tab -0.33619235:
\par p88 := 0.28168075,\tab -0.5372978,\tab -0.24879855:
\par p89 := 0.04724798,\tab -0.58137755,\tab -0.29950245:
\par p90 :=-0.54588885,\tab  0.23517195,\tab -0.2768272:
\par p91 :=-0.35441185,\tab  0.4632758,\tab -0.29950245:
\par p92 :=-0.142454,\tab  0.4844814,\tab -0.41823275:
\par p93 :=-0.4697953,\tab -0.28362035,\tab -0.3588676:
\par p94 :=-0.27044355,\tab -0.5029869,\tab -0.3221777:
\par p95 := 0.4548401,\tab  0.23517195,\tab -0.4095715:
\par p96 := 0.2640729,\tab  0.4632758,\tab -0.38154285:
\par p97 := 0.0284908,\tab  0.4844814,\tab -0.440908:
\par p98 := 0.35998885,\tab -0.28362035,\tab -0.46893665:
\par p99 := 0.1770964,\tab -0.5029869,\tab -0.38154285:
\par p100:=-0.47767005,\tab  0.16385005,\tab -0.41823275:
\par p101:=-0.2861924,\tab  0.3919539,\tab -0.440908:
\par p102:=-0.43064125,\tab -0.1567813,\tab -0.46893665:
\par p103:=-0.3369392,\tab -0.37614785,\tab -0.41823275:
\par p104:= 0.3521141,\tab  0.16385005,\tab -0.5283018:
\par p105:= 0.1613469,\tab  0.3919539,\tab -0.5002738:
\par p106:= 0.2934932,\tab -0.1567813,\tab -0.5649917:
\par p107:= 0.21625045,\tab -0.37614785,\tab -0.49161255:
\par p108:=-0.43364945,\tab  0.01413698,\tab -0.49161255:
\par p109:=-0.3478215,\tab  0.2422407,\tab -0.5002738:
\par p110:=-0.29778515,\tab -0.24930945,\tab -0.5283018:
\par p111:= 0.290485,\tab  0.01413698,\tab -0.58766695:
\par p112:= 0.2053675,\tab  0.2422407,\tab -0.57365295:
\par p113:= 0.14975415,\tab -0.24930945,\tab -0.58766695:
\par p114:=-0.3038009,\tab  0.0925275,\tab -0.57365295:
\par p115:=-0.16793725,\tab -0.17091815,\tab -0.61034285:
\par p116:= 0.1437384,\tab  0.0925275,\tab -0.6330181:
\par p117:= 0.00300786,\tab -0.17091815,\tab -0.6330181:
\par p118:=-0.1709448,\tab  0,\tab \tab \tab -0.6330181:
\par p119:= 0,\tab \tab  0,\tab \tab \tab -0.655694:
\par 
\par Ikosidodekaeder_abgestumpft_Vierecke:= [
\par p0,  p1,  p4,  p2,
\par p3,  p8,  p14, p7,
\par p5,  p10, p18, p11,
\par p6,  p12, p20, p13,
\par p9,  p17, p25, p16,
\par p15, p24, p35, p23,
\par p19, p28, p41, p29,
\par p21, p31, p44, p32,
\par p22, p33, p45, p34,
\par p26, p38, p50, p37,
\par p27, p40, p51, p39,
\par p30, p43, p54, p42,
\par p36, p48, p60, p49,
\par p46, p55, p67, p58,
\par p47, p59, p65, p53,
\par p52, p64, p73, p61,
\par p56, p62, p74, p68,
\par p57, p70, p81, p69,
\par p63, p75, p87, p76,
\par p66, p78, p90, p79,
\par p71, p82, p94, p83,
\par p72, p85, p95, p84,
\par p77, p89, p99, p88,
\par p80, p92, p101,p91,
\par p86, p96, p105,p97,
\par p93, p102,p110,p103,
\par p98, p107,p113,p106,
\par p100,p109,p114,p108,
\par p104,p111,p116,p112,
\par p115,p118,p119,p117
\par ]:
\par 
\par Ikosidodekaeder_abgestumpft_Sechsecke:= [
\par [p0,  p2,  p6,  p13, p8,  p3],
\par [p1,  p5,  p11, p17, p9,  p4],
\par [p7,  p14, p22, p34, p24, p15],
\par [p10, p19, p29, p40, p27, p18],
\par [p12, p21, p32, p43, p30, p20],
\par [p16, p25, p36, p49, p38, p26],
\par [p23, p35, p47, p53, p41, p28],
\par [p31, p37, p50, p62, p56, p44],
\par [p33, p46, p58, p70, p57, p45],
\par [p39, p51, p63, p76, p64, p52],
\par [p42, p54, p66, p79, p67, p55],
\par [p48, p61, p73, p85, p72, p60],
\par [p59, p71, p83, p89, p77, p65],
\par [p68, p74, p86, p97, p92, p80],
\par [p69, p81, p93, p103,p94, p82],
\par [p75, p88, p99, p107,p98, p87],
\par [p78, p91, p101,p109,p100,p90],
\par [p84, p95, p104,p112,p105,p96],
\par [p102,p108,p114,p118,p115,p110],
\par [p106,p113,p117,p119,p116,p111]
\par ]:
\par 
\par Ikosidodekaeder_abgestumpft_Zehnecke:= [
\par [p0, p3, p7,  p15, p23, p28, p19, p10, p5,  p1],
\par [p2, p4, p9,  p16, p26, p37, p31, p21, p12, p6],
\par [p8, p13,p20, p30, p42, p55, p46, p33, p22, p14],
\par [p11,p18,p27, p39, p52, p61, p48, p36, p25, p17],
\par [p24,p34,p45, p57, p69, p82, p71, p59, p47, p35],
\par [p29,p41,p53, p65, p77, p88, p75, p63, p51, p40],
\par [p32,p44,p56, p68, p80, p91, p78, p66, p54, p43],
\par [p38,p49,p60, p72, p84, p96, p86, p74, p62, p50],
\par [p58,p67,p79, p90, p100,p108,p102,p93, p81, p70],
\par [p64,p76,p87, p98, p106,p111,p104,p95, p85, p73],
\par [p83,p94,p103,p110,p115,p117,p113,p107,p99, p89],
\par [p92,p97,p105,p112,p116,p119,p118,p114,p109,p101]
\par ]:
\par 
\par Ikosidodekaeder_abgestumpft:= plot::Group3d(
\par    Name = "Ikosidodekaeders, abgestumpft",
\par    plot::SurfaceSet(Name="Vierecke", Ikosidodekaeder_abgestumpft_Vierecke, MeshListType = Quads, MeshVisible),
\par    plot::SurfaceSet(Name="Sechseck", Sechseck, MeshListType = TriangleFan, FillColorFunction=RGB::CinnabarGreen)     $ Sechseck in Ikosidodekaeder_abgestumpft_Sechsecke,
\par    plot::SurfaceSet(Name="Zehneck",  Zehneck,  MeshListType = TriangleFan, FillColorFunction=RGB::Gold)              $ Zehneck  in Ikosidodekaeder_abgestumpft_Zehnecke,
\par    plot::Polygon3d( Name="Sechseck, Rand", [Sechseck[3*i+1..3*i+3] $ i=0..5], Closed, LineColor = RGB::Black.[0.25]) $ Sechseck in Ikosidodekaeder_abgestumpft_Sechsecke,
\par    Scaling = Constrained
\par ):
\par 
\par plot( plot::Rotate3d( w, w=0..2*PI, Frames=100, Ikosidodekaeder_abgestumpft),
\par       Header                = "Archimedischer K\'f6rper: Ikosidodekaeder, abgestumpft",
\par       Axes                  = None,
\par       BackgroundStyle       = Pyramid,
\par       Width                 = 120,
\par       Height                = 120,
\par       BorderWidth           = 0.2,
\par       Footer                = "erstellt mit MuPAD Pro 3 - schule.mupad.de",
\par       FooterFont            = [8, Italic],
\par       FooterAlignment       = Right,
\par       plot::Scene3d::Margin = 0
\par ):
\par 
\par \pard\ri4\plain\f4\fs20\cf0\b _______________________________________________________________________________
\par \plain\f3\fs22\cf0 
\par \plain\f3\fs22\cf3\b Anmerkungen:\plain\f3\fs22\cf3 
\par \plain\f3\fs20\cf3\b 1\plain\f3\fs20\cf3 .  Weitere Anregungen zum Einsatz von MuPAD in der Lehre finden Sie auf unserem WebPortal
\par      \plain\f3\fs20\cf3\i MuPAD in Schule und Studium\plain\f3\fs20\cf3  unter: \plain\f3\fs20\cf1 http://schule.mupad.de\plain\f3\fs20\cf3  bzw. \plain\f3\fs20\cf1 http://studium.mupad.de\plain\f3\fs20\cf3 .
\par 
\par \plain\f3\fs20\cf3\b 2\plain\f3\fs20\cf3 . Weitere Informationen zu Archimedischen Platonischen K\'f6rper finden Sie auf der Webseite
\par     http://www.mathe.tu-freiberg.de/~hebisch/cafe/archimedische.html
\par \plain\f4\fs20\cf0\b _______________________________________________________________________________
\par \plain\f7\fs22\cf0 
\par }