Johnson Solid - Enumeration

Enumeration

Jn Solid name Net Image V E F F3 F4 F5 F6 F8 F10 Symmetry group
1 Square pyramid 5 8 5 4 1 C4v
(*44)
2 Pentagonal pyramid 6 10 6 5 1 C5v
(*55)
3 Triangular cupola 9 15 8 4 3 1 C3v
(*33)
4 Square cupola 12 20 10 4 5 1 C4v
(*44)
5 Pentagonal cupola 15 25 12 5 5 1 1 C5v
(*55)
6 Pentagonal rotunda 20 35 17 10 6 1 C5v
(*55)
7 Elongated triangular pyramid (or elongated tetrahedron) 7 12 7 4 3 C3v
(*33)
8 Elongated square pyramid (or augmented cube) 9 16 9 4 5 C4v
(*44)
9 Elongated pentagonal pyramid 11 20 11 5 5 1 C5v
(*55)
10 Gyroelongated square pyramid 9 20 13 12 1 C4v
(*44)
11 Gyroelongated pentagonal pyramid (or diminished icosahedron) 11 25 16 15 1 C5v
(*55)
12 Triangular bipyramid 5 9 6 6 D3h
(*223)
13 Pentagonal bipyramid 7 15 10 10 D5h
(*225)
14 Elongated triangular bipyramid 8 15 9 6 3 D3h
(*223)
15 Elongated square bipyramid
(or biaugmented cube)		 10 20 12 8 4 D4h
(*224)
16 Elongated pentagonal bipyramid 12 25 15 10 5 D5h
(*225)
17 Gyroelongated square bipyramid 10 24 16 16 D4d
(2*4)
18 Elongated triangular cupola 15 27 14 4 9 1 C3v
(*33)
19 Elongated square cupola
(diminished rhombicuboctahedron)		 20 36 18 4 13 1 C4v
(*44)
20 Elongated pentagonal cupola 25 45 22 5 15 1 1 C5v
(*55)
21 Elongated pentagonal rotunda 30 55 27 10 10 6 1 C5v
(*55)
22 Gyroelongated triangular cupola 15 33 20 16 3 1 C3v
(*33)
23 Gyroelongated square cupola 20 44 26 20 5 1 C4v
(*44)
24 Gyroelongated pentagonal cupola 25 55 32 25 5 1 1 C5v
(*55)
25 Gyroelongated pentagonal rotunda 30 65 37 30 6 1 C5v
(*55)
26 Gyrobifastigium 8 14 8 4 4 D2d
(2*2)
27 Triangular orthobicupola
(gyrate cuboctahedron)		 12 24 14 8 6 D3h
(*223)
28 Square orthobicupola 16 32 18 8 10 D4h
(*224)
29 Square gyrobicupola 16 32 18 8 10 D4d
(2*4)
30 Pentagonal orthobicupola 20 40 22 10 10 2 D5h
(*225)
31 Pentagonal gyrobicupola 20 40 22 10 10 2 D5d
(2*5)
32 Pentagonal orthocupolarotunda 25 50 27 15 5 7 C5v
(*55)
33 Pentagonal gyrocupolarotunda 25 50 27 15 5 7 C5v
(*55)
34 Pentagonal orthobirotunda
(gyrate icosidodecahedron)		 30 60 32 20 12 D5h
(*225)
35 Elongated triangular orthobicupola 18 36 20 8 12 D3h
(*223)
36 Elongated triangular gyrobicupola 18 36 20 8 12 D3d
(2*3)
37 Elongated square gyrobicupola
(gyrate rhombicuboctahedron)		 24 48 26 8 18 D4d
(2*4)
38 Elongated pentagonal orthobicupola 30 60 32 10 20 2 D5h
(*225)
39 Elongated pentagonal gyrobicupola 30 60 32 10 20 2 D5d
(2*5)
40 Elongated pentagonal orthocupolarotunda 35 70 37 15 15 7 C5v
(*55)
41 Elongated pentagonal gyrocupolarotunda 35 70 37 15 15 7 C5v
(*55)
42 Elongated pentagonal orthobirotunda 40 80 42 20 10 12 D5h
(*225)
43 Elongated pentagonal gyrobirotunda 40 80 42 20 10 12 D5d
(2*5)
44 Gyroelongated triangular bicupola
(2 chiral forms)		 18 42 26 20 6 D3
(223)
45 Gyroelongated square bicupola
(2 chiral forms)		 24 56 34 24 10 D4
(224)
46 Gyroelongated pentagonal bicupola
(2 chiral forms)		 30 70 42 30 10 2 D5
(225)
47 Gyroelongated pentagonal cupolarotunda
(2 chiral forms)		 35 80 47 35 5 7 C5(55)
48 Gyroelongated pentagonal birotunda
(2 chiral forms)		 40 90 52 40 12 D5
(225)
49 Augmented triangular prism 7 13 8 6 2 C2v
(*22)
50 Biaugmented triangular prism 8 17 11 10 1 C2v
(*22)
51 Triaugmented triangular prism 9 21 14 14 D3h
(*223)
52 Augmented pentagonal prism 11 19 10 4 4 2 C2v
(*22)
53 Biaugmented pentagonal prism 12 23 13 8 3 2 C2v
(*22)
54 Augmented hexagonal prism 13 22 11 4 5 2 C2v
(*22)
55 Parabiaugmented hexagonal prism 14 26 14 8 4 2 D2h
(*222)
56 Metabiaugmented hexagonal prism 14 26 14 8 4 2 C2v
(*22)
57 Triaugmented hexagonal prism 15 30 17 12 3 2 D3h
(*223)
58 Augmented dodecahedron 21 35 16 5 11 C5v
(*55)
59 Parabiaugmented dodecahedron 22 40 20 10 10 D5d
(2*5)
60 Metabiaugmented dodecahedron 22 40 20 10 10 C2v
(*22)
61 Triaugmented dodecahedron 23 45 24 15 9 C3v
(*33)
62 Metabidiminished icosahedron 10 20 12 10 2 C2v
(*22)
63 Tridiminished icosahedron 9 15 8 5 3 C3v
(*33)
64 Augmented tridiminished icosahedron 10 18 10 7 3 C3v
(*33)
65 Augmented truncated tetrahedron 15 27 14 8 3 3 C3v
(*33)
66 Augmented truncated cube 28 48 22 12 5 5 C4v
(*44)
67 Biaugmented truncated cube 32 60 30 16 10 4 D4h
(*224)
68 Augmented truncated dodecahedron 65 105 42 25 5 1 11 C5v
(*55)
69 Parabiaugmented truncated dodecahedron 70 120 52 30 10 2 10 D5d
(2*5)
70 Metabiaugmented truncated dodecahedron 70 120 52 30 10 2 10 C2v
(*22)
71 Triaugmented truncated dodecahedron 75 135 62 35 15 3 9 C3v
(*33)
72 Gyrate rhombicosidodecahedron 60 120 62 20 30 12 C5v
(*55)
73 Parabigyrate rhombicosidodecahedron 60 120 62 20 30 12 D5d
(2*5)
74 Metabigyrate rhombicosidodecahedron 60 120 62 20 30 12 C2v
(*22)
75 Trigyrate rhombicosidodecahedron 60 120 62 20 30 12 C3v
(*33)
76 Diminished rhombicosidodecahedron 55 105 52 15 25 11 1 C5v
(*55)
77 Paragyrate diminished rhombicosidodecahedron 55 105 52 15 25 11 1 C5v
(*55)
78 Metagyrate diminished rhombicosidodecahedron 55 105 52 15 25 11 1 Cs
(*11)
79 Bigyrate diminished rhombicosidodecahedron 55 105 52 15 25 11 1 Cs
(*11)
80 Parabidiminished rhombicosidodecahedron 50 90 42 10 20 10 2 D5d
(2*5)
81 Metabidiminished rhombicosidodecahedron 50 90 42 10 20 10 2 C2v
(*22)
82 Gyrate bidiminished rhombicosidodecahedron 50 90 42 10 20 10 2 Cs
(*11)
83 Tridiminished rhombicosidodecahedron 45 75 32 5 15 9 3 C3v
(*33)
84 Snub disphenoid
(Siamese dodecahedron)		 8 18 12 12 D2d
(2*2)
85 Snub square antiprism 16 40 26 24 2 D4d
(2*4)
86 Sphenocorona 10 22 14 12 2 C2v
(*22)
87 Augmented sphenocorona 11 26 17 16 1 Cs
(*11)
88 Sphenomegacorona 12 28 18 16 2 C2v
(*22)
89 Hebesphenomegacorona 14 33 21 18 3 C2v
(*22)
90 Disphenocingulum 16 38 24 20 4 D2d
(2*2)
91 Bilunabirotunda 14 26 14 8 2 4 D2h
(*222)
92 Triangular hebesphenorotunda 18 36 20 13 3 3 1 C3v
(*33)

Legend:

  • Jn – Johnson Solid Number
  • Net – Flattened (unfolded) image
  • V – Number of Vertices
  • E – Number of Edges
  • F – Number of Faces (total)
  • F3 – Number of 3-sided Faces
  • F4 – Number of 4-sided Faces
  • F5 – Number of 5-sided Faces
  • F6 – Number of 6-sided Faces
  • F8 – Number of 8-sided Faces
  • F10 – Number of 10-sided Faces

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