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单词 Johnson Solid
释义

Johnson Solid

The 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 pyramid

3. Triangular cupola

4. Square cupola

5. Pentagonal cupola

6. Pentagonal rotunda

7. Elongated triangular pyramid

8. Elongated square pyramid

9. Elongated pentagonal pyramid

10. Gyroelongated square pyramid

11. Gyroelongated pentagonal pyramid

12. Triangular dipyramid

13. Pentagonal dipyramid

14. Elongated triangular dipyramid

15. Elongated square dipyramid

16. Elongated pentagonal dipyramid

17. Gyroelongated square dipyramid

18. Elongated triangular cupola

19. Elongated square cupola

20. Elongated pentagonal cupola

21. Elongated pentagonal rotunda

22. Gyroelongated triangular cupola

23. Gyroelongated square cupola

24. Gyroelongated pentagonal cupola

25. Gyroelongated pentagonal rotunda

26. Gyrobifastigium

27. Triangular orthobicupola

28. Square orthobicupola

29. Square gyrobicupola

30. Pentagonal orthobicupola

31. Pentagonal gyrobicupola

32. Pentagonal orthocupolarontunda

33. Pentagonal gyrocupolarotunda

34. Pentagonal orthobirotunda

35. Elongated triangular orthobicupola

36. Elongated triangular gyrobicupola

37. Elongated square gyrobicupola

38. Elongated pentagonal orthobicupola

39. Elongated pentagonal gyrobicupola

40. Elongated pentagonal orthocupolarotunda

41. Elongated pentagonal gyrocupolarotunda

42. Elongated pentagonal orthobirotunda

43. Elongated pentagonal gyrobirotunda

44. Gyroelongated triangular bicupola

45. Gyroelongated square bicupola

46. Gyroelongated pentagonal bicupola

47. Gyroelongated pentagonal cupolarotunda

48. Gyroelongated pentagonal birotunda

49. Augmented triangular prism

50. Biaugmented triangular prism

51. Triaugmented triangular prism

52. Augmented pentagonal prism

53. Biaugmented pentagonal prism

54. Augmented hexagonal prism

55. Parabiaugmented hexagonal prism

56. Metabiaugmented hexagonal prism

57. Triaugmented hexagonal prism

58. Augmented dodecahedron

59. Parabiaugmented dodecahedron

60. Metabiaugmented dodecahedron

61. Triaugmented dodecahedron

62. Metabidiminished icosahedron

63. Tridiminished icosahedron

64. Augmented tridiminished icosahedron

65. Augmented truncated tetrahedron

66. Augmented truncated cube

67. Biaugmented truncated cube

68. Augmented truncated dodecahedron

69. Parabiaugmented truncated dodecahedron

70. Metabiaugmented truncated dodecahedron

71. Triaugmented truncated dodecahedron

72. Gyrate rhombicosidodecahedron

73. Parabigyrate rhombicosidodecahedron

74. Metabigyrate rhombicosidodecahedron

75. Trigyrate rhombicosidodecahedron

76. Diminished rhombicosidodecahedron

77. Paragyrate diminished rhombicosidodecahedron

78. Metagyrate diminished rhombicosidodecahedron

79. Bigyrate diminished rhombicosidodecahedron

80. Parabidiminished rhombicosidodecahedron

81. Metabidiminished rhombicosidodecahedron

82. Gyrate bidiminished rhombicosidodecahedron

83. Tridiminished rhombicosidodecahedron

84. Snub disphenoid

85. Snub square antiprism

86. Sphenocorona

87. Augmented sphenocorona

88. Sphenomegacorona

89. Hebesphenomegacorona

90. Disphenocingulum

91. Bilunabirotunda

92. Triangular hebesphenorotunda


The number of constituent -gons () for each Johnson solid are given in the following table.

       
141    473557   
25 1   4840 12   
343 1  4962    
445  1 50101    
5551  15114     
610 6  152442   
743    53832   
845    5445 2  
9551   5584 2  
10121    5684 2  
1115 1   57123 2  
126     585 11   
1310     5910 10   
1463    6010 10   
1584    6115 9   
16105    6210 2   
1716     635 3   
1849 1  647 3   
19413  1 6583 3  
205151  166125  5 
2110106  1671610  4 
22163 1  682551  11
23205  1 6930102  10
242551  17030102  10
2530 6  17135153  9
2644    72203012   
2786    73203012   
28810    74203012   
29810    75203012   
3010102   76152511  1
3110102   77152511  1
321557   78152511  1
331557   79152511  1
3420 12   80102010  2
35812    81102010  2
36812    82102010  2
37818    835159  3
3810202   8412     
3910202   85242    
4015157   86122    
4115157   87161    
42201012   88162    
43201012   89183    
44206    90204    
452410    91824   
4630102   9213331  

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.

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