Molde de poliedros

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posee moldes de poliedros

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Molde de poliedros

  1. 1. Paper Models of Polyhedra Gijs Korthals AltesPolyhedra are beautiful 3-D geometrical figures that have fascinated philosophers, mathematicians and artists for millennia
  2. 2. Copyrights © 1998-2001 Gijs.Korthals Altes All rights reserved .Its permitted to make copies for non-commercial purposes onlyemail: gijs@korthals.altes.net
  3. 3. 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
  4. 4. 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
  5. 5. Dodecahedron 1 3 7 11 59. 12 2 4 10 6. 8
  6. 6. Dodecahedron
  7. 7. Dodecahedron
  8. 8. Cube Tetrahedron
  9. 9. Cube 45 1 2 6 3 4 3 Tetrahedron 2 1
  10. 10. Octahedron
  11. 11. Icosahedron
  12. 12. Cuboctahedron
  13. 13. Icosidodecahedron
  14. 14. Truncated Tetrahedron
  15. 15. Truncated Octahedron
  16. 16. Truncated Cube
  17. 17. Truncated icosahedron
  18. 18. Truncated dodecahedron
  19. 19. Rhombicuboctahedron
  20. 20. Truncated cuboctahedron
  21. 21. Rombicosidodecahedron
  22. 22. Truncated Icosidodecahedron
  23. 23. Snub cube
  24. 24. Snub cubeRight-handed
  25. 25. Snub dodecahedron
  26. 26. Snub dodecahedronRight-handed
  27. 27. 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
  28. 28. 1 2
  29. 29. 3 4
  30. 30. 5 6
  31. 31. 8Octahemioctahedron type 1 type 2 7 13 11 5 12 6 2 10 1 3 4 14 13
  32. 32. Cubohemioctahedron
  33. 33. Small Rhombidodecahedron(small version)Fold the dotted lines forwardsFold the other lines
  34. 34. Small Rhombidodecahedron(large version)Fold the dotted lines forwardsFold the other lines A B F C E D
  35. 35. B A
  36. 36. C A
  37. 37. D A
  38. 38. E A
  39. 39. F A
  40. 40. Small dodecahemiododecahedronFolds the lines between thetriangles forwards. Folds theother lines backwards.
  41. 41. 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.
  42. 42. 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.
  43. 43. 1
  44. 44. 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
  45. 45. 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
  46. 46. 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
  47. 47. 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
  48. 48. 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
  49. 49. Pentagonale hexacontahedron
  50. 50. 12
  51. 51. 34
  52. 52. 56
  53. 53. 78
  54. 54. 910
  55. 55. 12
  56. 56. Pentagonallconssitetrahedron
  57. 57. Stella OctangulaType 1Type 2 Fold lines of type 1 backwards Fold lines of type 2 forwards
  58. 58. Fold the lines with a rightangle backwards fold the other lines forwardsCompound of twoCubes
  59. 59. Compound of Three Cubes(Small version)Fold the dotted liines forwardsFold the other lines backwards
  60. 60. Compound of Three Cubes (Small version) Fold the dotted liines forwards Fold the other lines backwards D A C CEE B F G G
  61. 61. A BC A A
  62. 62. A DE A A
  63. 63. AF A AG
  64. 64. 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
  65. 65. 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
  66. 66. B A BG C CG D D FF E E
  67. 67. B A A
  68. 68. C A AD A A
  69. 69. E A AF A A
  70. 70. G A A
  71. 71. 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
  72. 72. 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
  73. 73. 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
  74. 74. 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
  75. 75. 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
  76. 76. Pyramids
  77. 77. Pentagonal pyramid
  78. 78. Decahedron
  79. 79. Rhombic Dodecahedron
  80. 80. Great Rhombihexacron X X X X Fold the short lines forwards Fold the long lines backwards
  81. 81. Pentagonal Dipyramid
  82. 82. PentakisdodecahedronX X X X
  83. 83. ‘Dodecahedron’ A convex dodecahedron (not a platonic solid) constructed of 12 isosceles triangles
  84. 84. Hexakaidecahedron
  85. 85. ‘Icosahedron’ A convex icosahedron (not a platonic solid) constructed of 20 isosceles triangles
  86. 86. Icositetrahedron
  87. 87. Icosioctahedron
  88. 88. Tricontidihedron
  89. 89. Tricontihexahedron
  90. 90. Tetracontahedron
  91. 91. Hecatohedron
  92. 92. Third Stallation of the IcosahedronFold the dotted lines forwardsFold the other lines backwards X X X X
  93. 93. Third Stallation of the IcosahedronFold the dotted lines forwardsFold the other lines backwards X X X X
  94. 94. 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
  95. 95. Parts B-M
  96. 96. 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
  97. 97. Sixth Stallation of the Icosahedron(large version) B A
  98. 98. Sixth Stallation of the Icosahedron(large version) C A
  99. 99. Sixth Stallation of the Icosahedron(large version) D A
  100. 100. Sixth Stallation of the Icosahedron(large version) E A
  101. 101. Sixth Stallation of the Icosahedron(large version) A F
  102. 102. Sixth Stallation of the Icosahedron(large)
  103. 103. Sixth Stallation of the Icosahedron(large)
  104. 104. Sixth Stallation of the Icosahedron(large)
  105. 105. Sixth Stallation of the Icosahedron(large)
  106. 106. Sixth Stallation of the Icosahedron(large)
  107. 107. Sixth Stallation of the Icosahedron(large)
  108. 108. Seventh Stellation of the IcosahedronA D B B D C CB G A A G F FC I A A I H H
  109. 109. Seventh Stellation of the IcosahedronD E A A E J JE F D D F L LF B E E B N N
  110. 110. Seventh Stellation of the IcosahedronG H B B H O OH C G G C Q QI J C C J R R
  111. 111. Seventh Stellation of the IcosahedronJ D I I D K KK L J J L S SL E K K E M M
  112. 112. Seventh Stellation of the IcosahedronM N L L N T TN M O O M F FO G N N G P P
  113. 113. Seventh Stellation of the IcosahedronP Q O O Q T TQ H P P H R RR I Q Q I S S
  114. 114. Seventh Stellation of the IcosahedronS K R R K T TT P M M P S S
  115. 115. Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwards B B C CD AD E E F F
  116. 116. Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwards B A A
  117. 117. Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwards C A A
  118. 118. Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwards D A A
  119. 119. Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwards E A A
  120. 120. Eighth Stellation of the Icosahedron(Large version)Lold dotted lines forwardsFold other lines backwards A A F
  121. 121. 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
  122. 122. 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
  123. 123. Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards A B C F D E
  124. 124. Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards B A F C K G
  125. 125. Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards C A B D G H
  126. 126. Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards D A C E H I
  127. 127. Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards E A D F I J
  128. 128. Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards F A E B J K
  129. 129. Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards G B K C L H
  130. 130. Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards H C G D L I
  131. 131. Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards I D H E L J
  132. 132. Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards J E I F L K
  133. 133. Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards K F J B L G
  134. 134. Final Stellation of the icosahedronFold the dotted lines forwardsFold the other lines backwards L G K H J I
  135. 135. Triangular prisms
  136. 136. Pentagonal Prism
  137. 137. Pentagonal Antiprism
  138. 138. Octagonal Prism
  139. 139. Octagonal Antiprism
  140. 140. Pentagrammic PrismFold the dotted lines forwardsFold the other lines backwards
  141. 141. Pentagrammic AntiprismFold the dotted lines forwardsFold the other lines backwards
  142. 142. Hexagrammic PrismFold the dotted lines forwardsFold the other lines backwards
  143. 143. Hexagramic AntiprismFold the dotted lines forwardsFold the other lines backwards
  144. 144. Twisted rectangular prism (45 degrees)
  145. 145. Twisted rectangular prism (90 degrees)
  146. 146. Twisted rectangular prism (+ 45 -45 degrees)
  147. 147. Kaleidocyclus
  148. 148. Caleidocyclus 8
  149. 149. Caleidocyclus 10
  150. 150. Cylinder
  151. 151. 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
  152. 152. 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
  153. 153. Asymetric Cone
  154. 154. Square Cone
  155. 155. Square Cone
  156. 156. Paper Colour 1/ papier kleur1 noordelijke, oostelijke muur huis en de bodem north, east wall of the house and the floor
  157. 157. Paper Colour 1/ papier kleur1 dakkapel dormer-window zuidelijke en westelijke muur huis south and west wall house
  158. 158. paper colour 2 / papier kleur 2 (uitsnijden / cut-out)onderkantdak plus twee zijdentwo sides of the roof place dormer- window
  159. 159. 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
  160. 160. 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
  161. 161. 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
  162. 162. Globe
  163. 163. 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
  164. 164. Large Chevaux-de-friseThe other two parts are on the next two pages 3 1 1
  165. 165. 1 2 2
  166. 166. 3 2 2

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