Paper Models Of Polyhedra - ArvindGuptaToys
Paper Models of PolyhedraGijs Korthals AltesPolyhedra are beautiful 3-D geometrical figures that have fascinated philosophers,mathematicians and artists for millennia
Copyrights 1998-2001 Gijs.Korthals Altes All rights reserved .It's permitted to make copies for non-commercial purposes onlyemail: gijs@korthals.altes.net
Paper Models of PolyhedraPlatonic SolidsDodecahedronCube and TetrahedronOctahedronIcosahedronArchimedean SolidsCuboctahedronIcosidodecahedronTruncated TetrahedronTruncated OctahedronTruncated CubeTruncated Icosahedron (soccer ball)Truncated dodecahedronRhombicuboctahedronTruncated CuboctahedronRhombicosidodecahedronTruncated IcosidodecahedronSnub CubeSnub DodecahedronKepler-Poinsot PolyhedraGreat Stellated DodecahedronSmall Stellated DodecahedronGreat IcosahedronGreat DodecahedronOther Uniform hemioctahedronSmall RhombihexahedronSmall RhombidodecahedronS mall DodecahemiododecahedronSmall Ditrigonal IcosidodecahedronGreat DodecahedronCompoundsStella OctangulaCompound of Cube and OctahedronCompound of Dodecahedron and IcosahedronCompound of Two CubesCompound of Three CubesCompound of Five CubesCompound of Five OctahedraCompound of Five TetrahedraCompound of Truncated Icosahedron and Pentakisdodecahedron
Other PolyhedraPentagonal ntagonal PyramidDecahedronRhombic DodecahedronGreat RhombihexacronPentagonal DipyramidPentakisdodecahedronSmall TriakisoctahedronSmall Triambic IcosahedronPolyhedra Made of Isosceles TrianglesThird Stellation of the IcosahedronSixth Stellation of the IcosahedronSeventh Stellation of the IcosahedronEighth Stellation of the IcosahedronNinth Stellation of the IcosahedronFinal Stellation of the IcosahedronPrism and AntiprismTriangular PrismPentagonal PrismPe ntagonal AntiprismTriangular PrismOctagonal PrismOctagonal AntiprismPentagrammic PrismPentagrammic AntiprismHexagrammic PrismHexagrammic AntiprismTwisted Rectangular PrismKaleidocyclesHexagonal KaleidocycleOctagonal KaleidocycleDecagonal KaleidocycleOther Paper ModelsCylinderTapered CylinderConeSpecial Cones"Matryoska house""Matryoska house" 50%GlobeChevaux-de-frise
Dodecahedron1379.51221081146.
Dodecahedron
Dodecahedron
CubeTetrahedron
Cube4152632143Tetrahedron
Octahedron
Icosahedron
Cuboctahedron
Icosidodecahedron
Truncated Tetrahedron
Truncated Octahedron
Truncated Cube
Truncated icosahedron
Truncated dodecahedron
Rhombicuboctahedron
Truncated cuboctahedron
Rombicosidodecahedron
Truncated Icosidodecahedron
Snub cube
Snub cubeRight-handed
Snub dodecahedron
Snub dodecahedronRight-handed
Small Stellated DodecahedronOn this page a model outof one piece On the next pagesa model out of six pieces.Fold the long lines backwardsfold the short lines forwards
12
34
56
8Octahemioctahedrontype 1type 21371112562110341413
Cubohemioctahedron
Small Rhombidodecahedron(small version)Fold the dotted lines forwardsFold the other lines
Small Rhombidodecahedron(large version)Fold the dotted lines forwardsFold the other linesABCFED
BA
CA
DA
EA
FA
Small dodecahemiododecahedronFolds the lines between thetriangles forwards. Folds theother lines backwards.
Great Stellated Dodecahedronmade out of one piece of paper.Cut the lines between the longand the short sides of the triangles.Fold the long lines backwards andfold the short lines forwards.
Great Stellated Dodecahedronmade out of two pieces of paper.Cut the lines between the longand the short sides of the triangles.Fold the long lines backwards andfold the short lines forwards.This is piece one. On the next pageis piece two.1
1
Great Stellated Dodecahedronmade out of five pieces of paper.Cut the lines between the longand the short sides of the triangles.Fold the long lines backwards andfold the short lines forwards.N Next part P Previous partNP
Great Stellated Dodecahedronmade out of five pieces of paper.Cut the lines between the longand the short sides of the triangles.Fold the long lines backwards andfold the short lines forwards.N Next part P Previous partNP
Great Stellated Dodecahedronmade out of five pieces of paper.Cut the lines between the longand the short sides of the triangles.Fold the long lines backwards andfold the short lines forwards.N Next part P Previous partNP
Great Stellated Dodecahedronmade out of five pieces of paper.Cut the lines between the longand the short sides of the triangles.Fold the long lines backwards andfold the short lines forwards.N Next part P Previous partNP
Great Stellated Dodecahedronmade out of five pieces of paper.Cut the lines between the longand the short sides of the triangles.Fold the long lines backwards andfold the short lines forwards.N Next part P Previous partNP
Pentagonale hexacontahedron
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56
78
910
12
Pentagonallconssitetrahedron
Stella OctangulaType 1Type 2Fold lines of type 1backwardsFold lines of type 2forwards
Fold the lineswith a rightanglebackwardsfold the otherlines forwardsCompound of twoCubes
Compound of Three Cubes(Small version)Fold the dotted liines forwardsFold the other lines backwards
Compound of Three Cubes(Small version)Fold the dotted liines forwardsFold the other lines backwardsDACCEEBFGG
ABCAA
ADEAA
AFAAG
On this page a compound of five cubesmade of one piece of paper.On the next pages a compound of fivecubes made of 7 pieces of paper
Instructions:Cut and fold the piece(s) of paper.Glue the part without tabs around it last.This is the top part of piece F. This oneopposites the center part of piece A.Below an example of a partFold forwardsFold backwards
ABBGCCGDDFFEE
BAA
CAADAA
EAAFAA
GAA
Compound of five OctahedraIf you use paper in five different colorseach octahedron has a different colorColor 1AHDEGRCBIUMPdNFOQYLcWKaSJZXVTb
Compound of five OctahedraColor 2BKFGJWDALCNQOESRcdMPUTZXVbHIYa
Compound of five OctahedraColor 3CLIJDKMBYAORPQSFGNEHVXbWaTUZdc
Compound of five OctahedraColor 4DFKLOPBAGEISHRQUCTaJXZdcYVWbMN
Compound of five OctahedraColor 5EGNORHDAFBJTCVUIKWaSYXcZbLMdPQ
Pyramids
Pentagonal pyramid
Decahedron
Rhombic Dodecahedron
Great RhombihexacronXXXXFold the short lines forwardsFold the long lines backwards
Pentagonal Dipyramid
PentakisdodecahedronXXXX
‘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
Icositetrahedron
Icosioctahedron
Tricontidihedron
Tricontihexahedron
Tetracontahedron
Hecatohedron
Third Stallation of the IcosahedronFold the dotted lines forwardsFold the other lines backwardsXXXX
Third Stallation of the IcosahedronFold the dotted lines forwardsFold the other lines backwardsXXXX
Sixth 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:XXXX
Parts B-M
Sixth Stallation of the Icosahedron(large version)First glue the parts A until FGlue the 12 other parts on the ABCDEFCBDEAF
Sixth Stallation of the Icosahedron(large version)BA
Sixth Stallation of the Icosahedron(large version)CA
Sixth Stallation of the Icosahedron(large version)DA
Sixth Stallation of the Icosahedron(large version)EA
Sixth Stallation of the Icosahedron(large version)AF
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)
Seventh Stellation of the IcosahedronADBBDCBCGAAGFCFIAAIHH
Seventh Stellation of the IcosahedronDEAAEJEJFDDFLFLBEEBNN
Seventh Stellation of the IcosahedronGHBBHOHOCGGCQIQJCCJRR
Seventh Stellation of the IcosahedronJDIIDKKKLJJLSLSEKKEMM
Seventh Stellation of the IcosahedronMNLLNTNTMOOMFOFGNNGPP
Seventh Stellation of the IcosahedronPQOOQTQTHPPHRRRIQQISS
Seventh Stellation of the IcosahedronSKRRKTTTPMMPSS
Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwardsBBCCADDEEFF
Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwardsBAA
Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwardsCAA
Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwardsDAA
Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwardsEAA
Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwardsAAF
Ninth Stellation of the IcosahedronFold the dotted lines forwardsFold the other lines HBCDEAEAAFFABFBJKJKIJIJDE
LFGHFHJIJILJLJGK
Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwardsABCFDE
Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwardsBAFCKG
Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwardsCABDGH
Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwardsDACEHI
Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwardsEADFIJ
Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwardsFAEBJK
Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwardsGBKCLH
Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwardsHCGDLI
Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwardsIDHELJ
Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwardsJEIFLK
Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwardsKFJBLG
Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwardsLGKHJI
Triangular prisms
Pentagonal Prism
Pentagonal Antiprism
Octagonal Prism
Octagonal Antiprism
Pentagrammic PrismFold the dotted lines forwardsFold the other lines backwards
Pentagrammic AntiprismFold the dotted lines forwardsFold the other lines backwards
Hexagrammic PrismFold the dotted lines forwardsFold the other lines backwards
Hexagramic AntiprismFold the dotted lines forwardsFold the other lines backwards
Twisted rectangular prism (45 degrees)
Twisted rectangular prism (90 degrees)
Twisted rectangular prism ( 45 -45 degrees)
Kaleidocyclus
Caleidocyclus 8
Caleidocyclus 10
Cylinder
Tapered Cylinderlnxl c 2x 360.2.r2 h2r1. l /cd c.n/lr1r2r1 radiusr2 radiusc circumference of circle 1d circumference of circle 2x angel of the part of the large circlel radius of the large circleh height of the conei heigt of thetapered cylinder pi 3.1415
Conelxl c 2x 360.2.rr2 h2r. l /cr radiusc circumference of the circlex angel of the part of the large circlel radius of the large circleh height of the cone pi 3.1415
Asymetric Cone
Square Cone
Square Cone
Paper Colour 1/ papier kleur1noordelijke, oostelijke muur huis en de bodemnorth, east wall of the house and the floor
Paper Colour 1/ papier kleur1dakkapeldormer-windowzuidelijke en westelijke muur huissouth and west wall house
paper colour 2 / papier kleur 2(uitsnijden / cut-out)onderkantdak plus twee zijdentwo sides of the roofplacedormerwindow
onderkant dak/bottom rooffits around wallsdon't glue roof on thewallsTwee zijden dakTwo sides of the roofpaper colour 2 / papier kleur 2
Paper Colour 1/ papier kleur1Paper Colour 1/ papier kleur1dakkapeldormer-windowzuidelijke en westelijke muur huissouth and west wall housenoordelijke, oostelijke muur huis en de bodemnorth, east wall of the house and the floorPaper Colour 1/ papier kleur1Paper Colour 1/ papier kleur1dakkapeldormer-windowzuidelijke en westelijke muur huissouth and west wall housenoordelijke, oostelijke muur huis en de bodemnorth, east wall of the house and the floorPaper Colour 1/ papier kleur1Paper Colour 1/ papier kleur1dakkapeldormer-windowzuidelijke en westelijke muur huissouth and west wall housenoordelijke, oostelijke muur huis en de bodemnorth, east wall of the house and the floorPaper Colour 1/ papier kleur1Paper Colour 1/ papier kleur1dakkapeldormer-windowzuidelijke en westelijke muur huissouth and west wall housenoordelijke, oostelijke muur huis en de bodemnorth, east wall of the house and the floor
paper colour 2 / papier kleur 2onderkant dak/bottom rooffits around wallsdon't glue roof on thewalls(uitsnijden / cut-out)onderkantdak plus twee zijdentwo sides of the roofplacedormerwindowTwee zijden dakTwo sides of the roofpaper colour 2 / papier kleur 2paper colour 2 / papier kleur 2onderkant dak/bottom rooffits around wallsdon't glue roof on thewalls(uitsnijden / cut-out)onderkantdak plus twee zijdentwo sides of the roofplacedormerwindowTwee zijden dakTwo sides of the roofpaper colour 2 / papier kleur 2paper colour 2 / papier kleur 2onderkant dak/bottom rooffits around wallsdon't glue roof on thewalls(uitsnijden / cut-out)onderkantdak plus twee zijdentwo sides of the roofplacedormerwindowTwee zijden dakTwo sides of the roofpaper colour 2 / papier kleur 2paper colour 2 / papier kleur 2onderkant dak/bottom rooffits around wallsdon't glue roof on thewalls(uitsnijden / cut-out)onderkantdak plus twee zijdentwo sides of the roofplacedormerwindowTwee zijden dakTwo sides of the roofpaper colour 2 / papier kleur 2
Globe
311311223231131232112231232111323133232232311232
Large Chevaux-de-friseThe other two parts are on the next two pages311
122
322
made out of two pieces of paper. Cut the lines between the long and the short sides of the triangles. Fold the long
studied in the literature, is known as the homotopy method [6, 11, 50, 49, 51, 52, 7]. We illustrate the construction of simple polyhedra in Sections 2.5, 2.6, and 2.7. A similar deformation, again using Newton's method, allows us to construct truncated polyhedra from simple polyhedra, as shown in Section 2.8.
/ A Finite Element Method on Convex Polyhedra Figure 1: An object consisting of a single element falls on a slope. Due to the nonlinearity of the basis functions, nonlin-ear deformations are possible even for a single element. elements in order to obtain the elastic energy. Such meth-
Origami Burrs and Woven Polyhedra by Robert J. Lang This article and its successors originally appeared in Imagiro, an amateur press alliance, in 2000. In 1999 I attended the 2nd Scandinavian Origami Convention in Stockholm, where one of the attendees was Herman van Goubergen. Herman had some
Origami” [Fus90]. Kasahara/Takahama’s “Origami for the Connoisseur” [KT87] also has pictures of these polyhedra with a different numbering. I haven’t included modules for octagons or decagons. I’ve ma
The combinatorial theory of polyhedra investigates extremal properties of polyhedra by . their graphs to problems of estimation of the number of iterations and efficiency of algorithms of this type in linear . The general
Rose-Hulman Undergraduate Mathematics Journal Volume 16, No. 1, Spring 2015 Folding concave polygons into convex polyhedra: The L-Shape Emily Dinan Alice Nadeau Issac Odegard Kevin Hartshorn Abstract. Mathematicians have long been asking the question: Can a given convex polyhedron can be unf
CAPE Management of Business Specimen Papers: Unit 1 Paper 01 60 Unit 1 Paper 02 68 Unit 1 Paper 03/2 74 Unit 2 Paper 01 78 Unit 2 Paper 02 86 Unit 2 Paper 03/2 90 CAPE Management of Business Mark Schemes: Unit 1 Paper 01 93 Unit 1 Paper 02 95 Unit 1 Paper 03/2 110 Unit 2 Paper 01 117 Unit 2 Paper 02 119 Unit 2 Paper 03/2 134
pihak di bawah koordinasi Kementerian Pendidikan dan Kebudayaan, dan dipergunakan dalam tahap awal penerapan Kurikulum 2013. Buku ini merupakan “dokumen hidup” yang senantiasa diperbaiki, diperbaharui, dan dimutakhirkan sesuai dengan dinamika kebutuhan dan perubahan zaman. Masukan dari berbagai kalangan diharapkan dapat meningkatkan kualitas buku ini. Kontributor Naskah : Suyono . Penelaah .
