释义 |
Johnson SolidThe Johnson solids are the Convex Polyhedra having regular faces (with the exception of thecompletely regular Platonic Solids, the ``Semiregular''Archimedean Solids, and the two infinite families of Prisms andAntiprisms). There are 28 simple (i.e., cannot be dissected into two otherregular-faced polyhedra by a plane) regular-faced polyhedra in addition to the Prisms andAntiprisms (Zalgaller 1969), and Johnson (1966) proposed and Zalgaller (1969) proved that thereexist exactly 92 Johnson solids in all.
A database of solids and Vertex Nets of these solids is maintainedon the Bell Laboratories Netlib server, but a few errors exist inseveral entries. A concatenated and corrected version of the files is given by Weisstein, together with Mathematica (Wolfram Research, Champaign, IL) code to display the solids and nets. The following table summarizesthe names of the Johnson solids and gives their images and nets.
1. Square pyramid 2. Pentagonal pyramid3. Triangular cupola4. Square cupola5. Pentagonal cupola6. Pentagonal rotunda7. Elongated triangular pyramid8. Elongated square pyramid9. Elongated pentagonal pyramid10. Gyroelongated square pyramid11. Gyroelongated pentagonal pyramid12. Triangular dipyramid13. Pentagonal dipyramid14. Elongated triangular dipyramid15. Elongated square dipyramid16. Elongated pentagonal dipyramid17. Gyroelongated square dipyramid18. Elongated triangular cupola19. Elongated square cupola20. Elongated pentagonal cupola21. Elongated pentagonal rotunda22. Gyroelongated triangular cupola23. Gyroelongated square cupola24. Gyroelongated pentagonal cupola25. Gyroelongated pentagonal rotunda26. Gyrobifastigium27. Triangular orthobicupola28. Square orthobicupola29. Square gyrobicupola30. Pentagonal orthobicupola31. Pentagonal gyrobicupola32. Pentagonal orthocupolarontunda33. Pentagonal gyrocupolarotunda34. Pentagonal orthobirotunda35. Elongated triangular orthobicupola36. Elongated triangular gyrobicupola37. Elongated square gyrobicupola38. Elongated pentagonal orthobicupola39. Elongated pentagonal gyrobicupola40. Elongated pentagonal orthocupolarotunda41. Elongated pentagonal gyrocupolarotunda42. Elongated pentagonal orthobirotunda43. Elongated pentagonal gyrobirotunda44. Gyroelongated triangular bicupola45. Gyroelongated square bicupola46. Gyroelongated pentagonal bicupola47. Gyroelongated pentagonal cupolarotunda48. Gyroelongated pentagonal birotunda49. Augmented triangular prism50. Biaugmented triangular prism51. Triaugmented triangular prism52. Augmented pentagonal prism53. Biaugmented pentagonal prism54. Augmented hexagonal prism55. Parabiaugmented hexagonal prism56. Metabiaugmented hexagonal prism57. Triaugmented hexagonal prism58. Augmented dodecahedron59. Parabiaugmented dodecahedron60. Metabiaugmented dodecahedron61. Triaugmented dodecahedron62. Metabidiminished icosahedron63. Tridiminished icosahedron64. Augmented tridiminished icosahedron65. Augmented truncated tetrahedron66. Augmented truncated cube67. Biaugmented truncated cube68. Augmented truncated dodecahedron69. Parabiaugmented truncated dodecahedron70. Metabiaugmented truncated dodecahedron71. Triaugmented truncated dodecahedron72. Gyrate rhombicosidodecahedron73. Parabigyrate rhombicosidodecahedron74. Metabigyrate rhombicosidodecahedron75. Trigyrate rhombicosidodecahedron76. Diminished rhombicosidodecahedron77. Paragyrate diminished rhombicosidodecahedron78. Metagyrate diminished rhombicosidodecahedron79. Bigyrate diminished rhombicosidodecahedron80. Parabidiminished rhombicosidodecahedron81. Metabidiminished rhombicosidodecahedron82. Gyrate bidiminished rhombicosidodecahedron83. Tridiminished rhombicosidodecahedron84. Snub disphenoid85. Snub square antiprism86. Sphenocorona87. Augmented sphenocorona88. Sphenomegacorona89. Hebesphenomegacorona90. Disphenocingulum91. Bilunabirotunda92. Triangular hebesphenorotunda
The number of constituent -gons ( ) for each Johnson solid are given in the following table.  |  |  |  |  |  |  | | | | | | | | 1 | 4 | 1 | | | | | 47 | 35 | 5 | 7 | | | | 2 | 5 | | 1 | | | | 48 | 40 | | 12 | | | | 3 | 4 | 3 | | 1 | | | 49 | 6 | 2 | | | | | 4 | 4 | 5 | | | 1 | | 50 | 10 | 1 | | | | | 5 | 5 | 5 | 1 | | | 1 | 51 | 14 | | | | | | 6 | 10 | | 6 | | | 1 | 52 | 4 | 4 | 2 | | | | 7 | 4 | 3 | | | | | 53 | 8 | 3 | 2 | | | | 8 | 4 | 5 | | | | | 54 | 4 | 5 | | 2 | | | 9 | 5 | 5 | 1 | | | | 55 | 8 | 4 | | 2 | | | 10 | 12 | 1 | | | | | 56 | 8 | 4 | | 2 | | | 11 | 15 | | 1 | | | | 57 | 12 | 3 | | 2 | | | 12 | 6 | | | | | | 58 | 5 | | 11 | | | | 13 | 10 | | | | | | 59 | 10 | | 10 | | | | 14 | 6 | 3 | | | | | 60 | 10 | | 10 | | | | 15 | 8 | 4 | | | | | 61 | 15 | | 9 | | | | 16 | 10 | 5 | | | | | 62 | 10 | | 2 | | | | 17 | 16 | | | | | | 63 | 5 | | 3 | | | | 18 | 4 | 9 | | 1 | | | 64 | 7 | | 3 | | | | 19 | 4 | 13 | | | 1 | | 65 | 8 | 3 | | 3 | | | 20 | 5 | 15 | 1 | | | 1 | 66 | 12 | 5 | | | 5 | | 21 | 10 | 10 | 6 | | | 1 | 67 | 16 | 10 | | | 4 | | 22 | 16 | 3 | | 1 | | | 68 | 25 | 5 | 1 | | | 11 | 23 | 20 | 5 | | | 1 | | 69 | 30 | 10 | 2 | | | 10 | 24 | 25 | 5 | 1 | | | 1 | 70 | 30 | 10 | 2 | | | 10 | 25 | 30 | | 6 | | | 1 | 71 | 35 | 15 | 3 | | | 9 | 26 | 4 | 4 | | | | | 72 | 20 | 30 | 12 | | | | 27 | 8 | 6 | | | | | 73 | 20 | 30 | 12 | | | | 28 | 8 | 10 | | | | | 74 | 20 | 30 | 12 | | | | 29 | 8 | 10 | | | | | 75 | 20 | 30 | 12 | | | | 30 | 10 | 10 | 2 | | | | 76 | 15 | 25 | 11 | | | 1 | 31 | 10 | 10 | 2 | | | | 77 | 15 | 25 | 11 | | | 1 | 32 | 15 | 5 | 7 | | | | 78 | 15 | 25 | 11 | | | 1 | 33 | 15 | 5 | 7 | | | | 79 | 15 | 25 | 11 | | | 1 | 34 | 20 | | 12 | | | | 80 | 10 | 20 | 10 | | | 2 | 35 | 8 | 12 | | | | | 81 | 10 | 20 | 10 | | | 2 | 36 | 8 | 12 | | | | | 82 | 10 | 20 | 10 | | | 2 | 37 | 8 | 18 | | | | | 83 | 5 | 15 | 9 | | | 3 | 38 | 10 | 20 | 2 | | | | 84 | 12 | | | | | | 39 | 10 | 20 | 2 | | | | 85 | 24 | 2 | | | | | 40 | 15 | 15 | 7 | | | | 86 | 12 | 2 | | | | | 41 | 15 | 15 | 7 | | | | 87 | 16 | 1 | | | | | 42 | 20 | 10 | 12 | | | | 88 | 16 | 2 | | | | | 43 | 20 | 10 | 12 | | | | 89 | 18 | 3 | | | | | 44 | 20 | 6 | | | | | 90 | 20 | 4 | | | | | 45 | 24 | 10 | | | | | 91 | 8 | 2 | 4 | | | | 46 | 30 | 10 | 2 | | | | 92 | 13 | 3 | 3 | 1 | | | See also Antiprism, Archimedean Solid, Convex Polyhedron, Kepler-Poinsot Solid,Polyhedron, Platonic Solid, Prism, Uniform Polyhedron References
Bell Laboratories. http://netlib.bell-labs.com/netlib/polyhedra/.Bulatov, V. ``Johnson Solids.'' http://www.physics.orst.edu/~bulatov/polyhedra/johnson/. Cromwell, P. R. Polyhedra. New York: Cambridge University Press, pp. 86-92, 1997. Hart, G. W. ``NetLib Polyhedra DataBase.'' http://www.li.net/~george/virtual-polyhedra/netlib-info.html. Holden, A. Shapes, Space, and Symmetry. New York: Dover, 1991. Hume, A. Exact Descriptions of Regular and Semi-Regular Polyhedra and Their Duals. Computer Science Technical Report #130. Murray Hill, NJ: AT&T Bell Laboratories, 1986. Johnson, N. W. ``Convex Polyhedra with Regular Faces.'' Canad. J. Math. 18, 169-200, 1966. Pugh, A. ``Further Convex Polyhedra with Regular Faces.'' Ch. 3 in Polyhedra: A Visual Approach. Berkeley, CA: University of California Press, pp. 28-35, 1976. Weisstein, E. W. ``Johnson Solids.'' Mathematica notebook JohnsonSolids.m.
Weisstein, E. W. ``Johnson Solid Netlib Database.'' Mathematica notebook JohnsonSolids.dat.
Zalgaller, V. Convex Polyhedra with Regular Faces. New York: Consultants Bureau, 1969. |