Molde de poliedros
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Molde de poliedros

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Molde de poliedros Molde de poliedros Document Transcript

  • Paper Models of Polyhedra Gijs 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 .Its 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 PolyhedraTetrahemihexahedronOctahemioctahedronCubohemioctahedronSmall 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 HexecontahedronPentagonalconsitetrahedronPyramidPentagonal 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
  • Dodecahedron 1 3 7 11 59. 12 2 4 10 6. 8
  • Dodecahedron
  • Dodecahedron
  • Cube Tetrahedron
  • Cube 45 1 2 6 3 4 3 Tetrahedron 2 1
  • 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
  • 1 2
  • 3 4
  • 5 6
  • 8Octahemioctahedron type 1 type 2 7 13 11 5 12 6 2 10 1 3 4 14 13
  • Cubohemioctahedron
  • Small Rhombidodecahedron(small version)Fold the dotted lines forwardsFold the other lines
  • Small Rhombidodecahedron(large version)Fold the dotted lines forwardsFold the other lines A B F C E D
  • B A
  • C A
  • D A
  • E A
  • F A
  • 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. 1Cut 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
  • 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 part NP
  • 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 part NP
  • 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 part NP
  • 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 part NP
  • 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 part NP
  • Pentagonale hexacontahedron
  • 12
  • 34
  • 56
  • 78
  • 910
  • 12
  • Pentagonallconssitetrahedron
  • Stella OctangulaType 1Type 2 Fold lines of type 1 backwards Fold lines of type 2 forwards
  • Fold the lines with a rightangle backwards fold the other lines 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 forwards Fold the other lines backwards D A C CEE B F G G
  • A BC A A
  • A DE A A
  • AF A AG
  • On this page a compound of five cubes made 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 part Fold forwards Fold backwards
  • B A BG C CG D D FF E E
  • B A A
  • C A AD A A
  • E A AF A A
  • G A A
  • Compound of five Octahedra If you use paper in five different colors each octahedron has a different color Color 1 A D H G E R C IB U M d P F N O Y QL c K T W a S J X ZV b
  • Compound of five Octahedra Color 2 B F K J G W D A C L N O Q S E R d cM P T Y U Z V X H bI a
  • Compound of five Octahedra Color 3 C I L D J K B M Y A O P R Q F S G NE H X Z V b W a T dU c
  • Compound of five Octahedra Color 4 D K F O L P A BE G I H S R U Q C TJ a Z b X d Y c V MW N
  • Compound of five Octahedra Color 5 E N G R O H D FA B J C T V I U K aW S X d Y c Z b L PM Q
  • Pyramids
  • Pentagonal pyramid
  • Decahedron
  • Rhombic Dodecahedron
  • Great Rhombihexacron X X X X Fold the short lines forwards Fold the long lines backwards
  • Pentagonal Dipyramid
  • PentakisdodecahedronX X X X
  • ‘Dodecahedron’ A convex dodecahedron (not a platonic solid) constructed of 12 isosceles triangles
  • Hexakaidecahedron
  • ‘Icosahedron’ A convex icosahedron (not a platonic solid) constructed of 20 isosceles triangles
  • Icositetrahedron
  • Icosioctahedron
  • Tricontidihedron
  • Tricontihexahedron
  • Tetracontahedron
  • Hecatohedron
  • Third Stallation of the IcosahedronFold the dotted lines forwardsFold the other lines backwards X X X X
  • Third Stallation of the IcosahedronFold the dotted lines forwardsFold the other lines backwards X X X X
  • Sixth Stallation of the Icosahedron (small version)Fold the dotted lines forwardsFold the other lines backwardsFirst glue part AGlue the parts A-M on A Part A: X X X X
  • Parts B-M
  • Sixth Stallation of the Icosahedron(large version)First glue the parts A until FGlue the 12 other parts on the ABCDEF C B D E A F
  • Sixth Stallation of the Icosahedron(large version) B A
  • Sixth Stallation of the Icosahedron(large version) C A
  • Sixth Stallation of the Icosahedron(large version) D A
  • Sixth Stallation of the Icosahedron(large version) E A
  • Sixth Stallation of the Icosahedron(large version) A F
  • 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 IcosahedronA D B B D C CB G A A G F FC I A A I H H
  • Seventh Stellation of the IcosahedronD E A A E J JE F D D F L LF B E E B N N
  • Seventh Stellation of the IcosahedronG H B B H O OH C G G C Q QI J C C J R R
  • Seventh Stellation of the IcosahedronJ D I I D K KK L J J L S SL E K K E M M
  • Seventh Stellation of the IcosahedronM N L L N T TN M O O M F FO G N N G P P
  • Seventh Stellation of the IcosahedronP Q O O Q T TQ H P P H R RR I Q Q I S S
  • Seventh Stellation of the IcosahedronS K R R K T TT P M M P S S
  • Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwards B B C CD AD E E F F
  • Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwards B A A
  • Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwards C A A
  • Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwards D A A
  • Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwards E A A
  • Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwards A A F
  • Ninth Stellation of the Icosahedron Fold the dotted lines forwards Fold the other lines backwards C F B A B A F CA F B C E G E G D K D K C F B C A A A AC D D E D E H I H I G H G H B C D E A A A AE F F B F B J K J K I J I J D E
  • K L B G B G C CG C H C H D H D L I L I K L H F D K D KI E J L E L J I J I L E L E H F G K B G B GK L F H F H J I J I L J L J G K
  • Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards A B C F D E
  • Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards B A F C K G
  • Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards C A B D G H
  • Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards D A C E H I
  • Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards E A D F I J
  • Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards F A E B J K
  • Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards G B K C L H
  • Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards H C G D L I
  • Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards I D H E L J
  • Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards J E I F L K
  • Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards K F J B L G
  • Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards L G K H J I
  • 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 Cylinder l n x 2 2 l= r + h c=2 r1 x = 360.2. . l /c d=c.n/lr1 r1 = radius r2 = radius r2 c = circumference of circle 1 d = circumference of circle 2 x =angel of the part of the large circle l = radius of the large circle h = height of the cone i = heigt of the tapered cylinder = pi = 3.1415
  • Cone l x 2 2 l= r + h c=2 r x = 360.2. . l /c r = radius c = circumference of the circle r x =angel of the part of the large circle l = radius of the large circle h = height of the cone = pi = 3.1415
  • Asymetric Cone
  • Square Cone
  • Square Cone
  • Paper Colour 1/ papier kleur1 noordelijke, oostelijke muur huis en de bodem north, east wall of the house and the floor
  • Paper Colour 1/ papier kleur1 dakkapel dormer-window zuidelijke en westelijke muur huis south and west wall house
  • paper colour 2 / papier kleur 2 (uitsnijden / cut-out)onderkantdak plus twee zijdentwo sides of the roof place dormer- window
  • onderkant dak/ bottom roof fits around walls dont glue roof on the walls Twee zijden dakTwo sides of the roofpaper colour 2 / papier kleur 2
  • Paper Colour 1/ papier kleur1 Paper Colour 1/ papier kleur1 dakkapel dormer-window zuidelijke en westelijke muur huis south and west wall house noordelijke, oostelijke muur huis en de bodem north, east wall of the house and the floor Paper Colour 1/ papier kleur1 Paper Colour 1/ papier kleur1 dakkapel dormer-window zuidelijke en westelijke muur huis south and west wall house noordelijke, oostelijke muur huis en de bodem north, east wall of the house and the floor Paper Colour 1/ papier kleur1 Paper Colour 1/ papier kleur1 dakkapel dormer-window zuidelijke en westelijke muur huis south and west wall house noordelijke, oostelijke muur huis en de bodem north, east wall of the house and the floorPaper Colour 1/ papier kleur1 Paper Colour 1/ papier kleur1 dakkapel dormer-window zuidelijke en westelijke muur huis south and west wall house noordelijke, oostelijke muur huis en de bodem north, east wall of the house and the floor
  • paper colour 2 / papier kleur 2 onderkant dak/ bottom roof fits around walls dont glue roof on the walls (uitsnijden / cut-out) onderkantdak plus twee zijden two sides of the roof place dormer- window Twee zijden dak Two sides of the roof paper colour 2 / papier kleur 2 paper colour 2 / papier kleur 2 onderkant dak/ bottom roof fits around walls dont glue roof on the walls (uitsnijden / cut-out)onderkantdak plus twee zijdentwo sides of the roof place dormer- window Twee zijden dak Two sides of the roof paper colour 2 / papier kleur 2 paper colour 2 / papier kleur 2 onderkant dak/ bottom roof fits around walls dont glue roof on the walls (uitsnijden / cut-out) onderkantdak plus twee zijden two sides of the roof place dormer- window Twee zijden dak Two sides of the roof paper colour 2 / papier kleur 2 paper colour 2 / papier kleur 2 onderkant dak/ bottom roof fits around walls dont glue roof on the walls (uitsnijden / cut-out) onderkantdak plus twee zijden two sides of the roof place dormer- window Twee zijden dak Two sides of the roof paper colour 2 / papier kleur 2
  • Globe
  • 3 1 3 1 2 2 3 1 31 2 2 3 1 3 1 2 2 3 1 3 1 3 3 1 2 21 2 2 3 1 3 1 2 2 3 1 31 2 2 3 1 3 1 2 2
  • Large Chevaux-de-friseThe other two parts are on the next two pages 3 1 1
  • 1 2 2
  • 3 2 2