Paper Models of Polyhedra - Arvind Gupta

1 Paper Models of PolyhedraGijs Korthals AltesPolyhedra are beautiful 3-D geometrical figures that have fascinated philosophers, mathematicians and artists for millenniaCopyrights 1998-2001 Altes All rights reserved . It's permitted to make copies for non-commercial purposes onlyemail: Models of PolyhedraPlatonic Solids Archimedean Solids Kepler-Poinsot PolyhedraOther Uniform Polyhedra CompoundsDodecahedron Cube and Tetrahedron Octahedron Icosahedron Cuboctahedron Icosidodecahedron Truncated Tetrahedron Truncated Octahedron Truncated Cube Truncated Icosahedron (soccer ball)

2 Truncated dodecahedron Rhombicuboctahedron Truncated Cuboctahedron Rhombicosidodecahedron Truncated Icosidodecahedron Snub Cube Snub Dodecahedron Great Stellated DodecahedronSmall Stellated DodecahedronGreat Icosahedron Great DodecahedronTetrahemihexahedronOctahemio ctahedronCubohemioctahedronSmall Rhombihexahedron Small DodecahemiododecahedronSmall Ditrigonal IcosidodecahedronGreat DodecahedronStella OctangulaCompound of Cube and OctahedronCompound of Dodecahedron and IcosahedronCompound of Two CubesCompound of Three Cubes Compound of Five Cubes Compound of Five Octahedra Compound of Five Tetrahedra Compound of Truncated Icosahedron and PentakisdodecahedronSmall RhombidodecahedronOther PolyhedraPrism and AntiprismKaleidocyclesOther Paper ModelsPentagonal HexecontahedronPentagonalconsitetrahedro nPyramidPentagonal PyramidDecahedronRhombic DodecahedronGreat RhombihexacronPentagonal DipyramidPentakisdodecahedronSmall TriakisoctahedronSmall Triambic IcosahedronPolyhedra Made of Isosceles TrianglesThird Stellation of the IcosahedronSixth Stellation of the IcosahedronSeventh

3 Stellation of the IcosahedronEighth Stellation of the IcosahedronNinth Stellation of the IcosahedronFinal Stellation of the IcosahedronTriangular PrismPentagonal PrismPentagonal AntiprismTriangular PrismOctagonal PrismOctagonal AntiprismPentagrammic PrismPentagrammic AntiprismHexagrammic PrismHexagrammic AntiprismTwisted Rectangular Prism Hexagonal KaleidocycleOctagonal KaleidocycleDecagonal KaleidocycleCylinder Tapered CylinderConeSpecial Cones"Matryoska house""Matryoska house" 50% TetrahedronTruncated OctahedronTruncated CubeTruncated icosahedronTruncated dodecahedronRhombicuboctahedronTruncated cuboctahedronRombicosidodecahedronTrunca ted IcosidodecahedronSnub cubeSnub cubeRight-handedSnub dodecahedronSnub dodecahedronRight-handedSmall Stellated DodecahedronOn this page a model outof one piece On the next pagesa model out of six the long lines backwardsfold the short lines forwards 12345612345671181312141310type 1type 2 OctahemioctahedronCubohemioctahedronSmal l Rhombidodecahedron(small version)

4 Fold the dotted lines forwardsFold the other linesASmall Rhombidodecahedron(large version)Fold the dotted lines forwardsFold the other linesBCDEFBACADAEAFAF olds the lines between the triangles forwards. Folds theother lines dodecahemiododecahedronGreat Stellated Dodecahedronmade out of one piece of the lines between the longand the short sides of the the long lines backwards and fold the short lines Stellated Dodecahedronmade out of two pieces of the lines between the longand the short sides of the the long lines backwards and fold the short lines is piece one.

5 On the next pageis piece Stellated Dodecahedronmade out of five pieces of the lines between the longand the short sides of the the long lines backwards and fold the short lines Next part P= Previous partNPGreat Stellated Dodecahedronmade out of five pieces of the lines between the longand the short sides of the the long lines backwards and fold the short lines Next part P= Previous partNPGreat Stellated Dodecahedronmade out of five pieces of the lines between the longand the short sides of the the long lines backwards and fold the short lines Next part P= Previous partNPGreat Stellated Dodecahedronmade out of five pieces of the lines between the longand the short sides of the the long lines backwards and fold the short lines Next part P= Previous partNPGreat Stellated Dodecahedronmade out of five pieces of the lines between the longand the short sides of the the long lines backwards and fold the short lines Next part P= Previous partNPPentagonale hexacontahedron1234567891012 PentagonallconssitetrahedronStella OctangulaType 1 Type 2 Fold

6 Lines of type 1backwardsFold lines of type 2 forwardsFold the lineswith a rightangle backwards fold the other lines forwardsCompound of twoCubesCompound of Three Cubes(Small version)Fold the dotted liines forwardsFold the other lines backwardsDCCBEEFGGAC ompound of Three Cubes(Small version)Fold the dotted liines forwardsFold the other lines backwardsABAACADAAEAFGAAOn this page a compound of five cubes made of one piece of the next pages a compound of five cubes made of 7 pieces of paperInstructions:Cut and fold the piece(s) of the part without tabs around it is the top part of piece F.

7 This one opposites the center part of piece A. Below an example of a part Fold forwardsFold backwardsGGBBACCDDEEFFAABCDAAAAAAFEAAAAG AHMPWaCompound of five OctahedraColor 1If you use Paper in five different colorseach octahedron has a different colorBCDEGILNOFQRUYdcJKVXTZSbBKNQUZC ompound of five OctahedraColor 2 ACJDLEOMFGPRWdScHTVIXYabCLORVbCompound of five OctahedraColor 3 ABKDIJQGHSMEFNPYTXWUaZdcDFISXdCompound of five OctahedraColor 4 AEBGHCJKLOPURTaQZVWYMNbcEGJTYcCompound of five OctahedraColor 5 ADFBCIKNORHWVUSaXZMLbdPQPyramidsPentagon al pyramidDecahedronRhombic DodecahedronXXXXG

8 Reat RhombihexacronFold the short lines forwardsFold the long lines backwardsPentagonal DipyramidXXXXP entakisdodecahedron Dodecahedron A convex dodecahedron(not a platonic solid)constructed of 12isosceles triangles Hexakaidecahedron Icosahedron A convex icosahedron(not a platonic solid)constructed of 20isosceles triangles IcositetrahedronIcosioctahedronTricontid ihedronTricontihexahedronTetracontahedro nHecatohedronThird Stallation of the IcosahedronXXXXFold the dotted lines forwardsFold the other lines backwardsThird Stallation of the IcosahedronXXXXFold the dotted lines forwardsFold the other lines backwardsSixth Stallation of the Icosahedron(small version)Fold the dotted lines forwardsFold the other lines backwardsFirst glue part AGlue the parts A-M on APart A.

9 XXXXP arts B-MFBCDEAS ixth Stallation of the Icosahedron(large version)First glue the parts A until FGlue the 12 other parts on the ABCDEFABS ixth Stallation of the Icosahedron(large version)ACSixth Stallation of the Icosahedron(large version)DASixth Stallation of the Icosahedron(large version)AESixth Stallation of the Icosahedron(large version)AFSixth Stallation of the Icosahedron(large version)Sixth Stallation of the Icosahedron(large)Sixth Stallation of the Icosahedron(large)Sixth Stallation of the Icosahedron(large)Sixth Stallation of the Icosahedron(large)Sixth Stallation of the Icosahedron(large)Sixth Stallation of the Icosahedron(large)

10 ABCS eventh Stellation of the IcosahedronDGIBAABAACFHCFHDGIDEFEFBADEAD EJLNJLNEFBS eventh Stellation of the IcosahedronGHIHCJBGCBGCOQROQRHCJS eventh Stellation of the IcosahedronJKLDEIJKIJKKSMKSMDLELS eventh Stellation of the IcosahedronMNONMGLONLONTFPTFPNMGS eventh Stellation of the IcosahedronPQRQHIOPQOPQTRSTRSQHIS eventh Stellation of the IcosahedronSTKRMRMTSTSKPPS eventh Stellation of the IcosahedronBCCDDEEFFBAE ighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwardsBAAE ighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwardsCAAE ighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwardsDAAE ighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwardsAEAE ighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwardsFAAE ighth Stellation of the Icosahedron(Large version)