The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the
exception of the completely regular Platonic solids, the "semiregular" Archimedean solids, and the two infinite families of prisms and
antiprisms). There are 28 simple (i.e., cannot be dissected into two other regularfaced polyhedra by a
plane) regularfaced polyhedra in addition to the prisms and antiprisms (Zalgaller
1969), and Johnson (1966) proposed and Zalgaller (1969) proved that there exist exactly 92 Johnson solids in all.
There is a nearJohnson solid which can be constructed by inscribing regular nonagons inside the eight triangular faces of a
regular octahedron, then joining the free edges to the 24 triangles and finally the remaining edges of the triangles to six
squares, with one square for each octahedral vertex. It turns out that the triangles are not quite equilateral, making the
edges that bound the squares a slightly different length from that of the enneagonal edge. However, because the differences
in edge lengths are so small, the flexing of an average model allows the solid to be constructed with all edges equal (Olshevsky).
A database of solids and polyhedron vertex nets of these solids is maintained on the Bell
Laboratories Netlib server (http://netlib.belllabs.com/netlib/polyhedra/), but a few errors exist in several entries. A concatenated and corrected version of the files is given by Weisstein, together with Mathematica code to
display the solids and nets. The following table summarizes the 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 orthocupolarotunda
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
