Bruker:Berntisso/Sandkasse
Utseende
Dette er en komplett liste over alle Johnson-legemer.
Jn | Navn på legeme | Brettet utover en 2D-flate | Image | V | E | F | F3 | F4 | F5 | F6 | F8 | F10 | Symmetri-gruppe | Symmetri-tall |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | Kvadratisk pyramide | ![]() |
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5 | 8 | 5 | 4 | 1 | C4v, [4], (*44) | 8 | ||||
2 | Pentagonal pyramide | ![]() |
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6 | 10 | 6 | 5 | 1 | C5v, [5], (*55) | 10 | ||||
3 | Trekantet kuppel | ![]() |
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9 | 15 | 8 | 4 | 3 | 1 | C3v, [3], (*33) | 6 | |||
4 | Kvadratisk kuppel | ![]() |
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12 | 20 | 10 | 4 | 5 | 1 | C4v, [4], (*44) | 8 | |||
5 | Pentagonal kuppel | ![]() |
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15 | 25 | 12 | 5 | 5 | 1 | 1 | C5v, [5], (*55) | 10 | ||
6 | Pentagonal rotunde | ![]() |
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20 | 35 | 17 | 10 | 6 | 1 | C5v, [5], (*55) | 10 | |||
7 | Forlenget trekantet pyramide | ![]() |
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7 | 12 | 7 | 4 | 3 | C3v, [3], (*33) | 6 | ||||
8 | Forlenget kvadratisk pyramide | ![]() |
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9 | 16 | 9 | 4 | 5 | C4v, [4], (*44) | 8 | ||||
9 | Forlenget pentagonal pyramide | ![]() |
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11 | 20 | 11 | 5 | 5 | 1 | C5v, [5], (*55) | 10 | |||
10 | Gyroforlenget kvadratisk pyramide | ![]() |
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9 | 20 | 13 | 12 | 1 | C4v, [4], (*44) | 8 | ||||
11 | Gyroforlenget kvadratisk pyramide | ![]() |
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11 | 25 | 16 | 15 | 1 | C5v, [5], (*55) | 10 | ||||
12 | Trekantet bipyramide | ![]() |
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5 | 9 | 6 | 6 | D3h, [3,2], (*223) | 12 | |||||
13 | Pentagonal bipyramide | ![]() |
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7 | 15 | 10 | 10 | D5h, [5,2], (*225) | 20 | |||||
14 | Forlenget trekantet bipyramide | ![]() |
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8 | 15 | 9 | 6 | 3 | D3h, [3,2], (*223) | 12 | ||||
15 | Forlenget kvadratisk bipyramide | ![]() |
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10 | 20 | 12 | 8 | 4 | D4h, [4,2], (*224) | 16 | ||||
16 | Forlenget pentagonal bipyramide | ![]() |
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12 | 25 | 15 | 10 | 5 | D5h, [5,2], (*225) | 20 | ||||
17 | Gyroforlenget kvadratisk bipyramide | ![]() |
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10 | 24 | 16 | 16 | D4d, [2+,8], (2*4) | 16 | |||||
18 | Forlenget trekantet kuppel | ![]() |
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15 | 27 | 14 | 4 | 9 | 1 | C3v, [3], (*33) | 6 | |||
19 | Forlenget kvadratisk kuppel | ![]() |
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20 | 36 | 18 | 4 | 13 | 1 | C4v, [4], (*44) | 8 | |||
20 | Forlenget pentagonal kuppel | ![]() |
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25 | 45 | 22 | 5 | 15 | 1 | 1 | C5v, [5], (*55) | 10 | ||
21 | Forlenget pentagonal rotunde | ![]() |
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30 | 55 | 27 | 10 | 10 | 6 | 1 | C5v, [5], (*55) | 10 | ||
22 | Gyroforlenget trekantet kuppel | ![]() |
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15 | 33 | 20 | 16 | 3 | 1 | C3v, [3], (*33) | 6 | |||
23 | Gyroforlenget kvadratisk kuppel | ![]() |
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20 | 44 | 26 | 20 | 5 | 1 | C4v, [4], (*44) | 8 | |||
24 | Gyroforlenget pentagonal kuppel | ![]() |
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25 | 55 | 32 | 25 | 5 | 1 | 1 | C5v, [5], (*55) | 10 | ||
25 | Gyroforlenget pentagonal rotunde | ![]() |
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30 | 65 | 37 | 30 | 6 | 1 | C5v, [5], (*55) | 10 | |||
26 | Gyrobifastigium | ![]() |
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8 | 14 | 8 | 4 | 4 | D2d, [2+,4], (2*2) | 8 | ||||
27 | Trekantet ortobikuppel | ![]() |
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12 | 24 | 14 | 8 | 6 | D3h, [3,2], (*223) | 12 | ||||
28 | Kvadratisk ortobikuppel | ![]() |
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16 | 32 | 18 | 8 | 10 | D4h, [4,2], (*224) | 16 | ||||
29 | Kvadratisk gyrobikuppel | ![]() |
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16 | 32 | 18 | 8 | 10 | D4d, [2+,8], (2*4) | 16 | ||||
30 | Pentagonal ortobikuppel | ![]() |
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20 | 40 | 22 | 10 | 10 | 2 | D5h, [5,2], (*225) | 20 | |||
31 | Pentagonal gyrobikuppel | ![]() |
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20 | 40 | 22 | 10 | 10 | 2 | D5d, [2+,10], (2*5) | 20 | |||
32 | Pentagonal ortokuppelrotunde | ![]() |
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25 | 50 | 27 | 15 | 5 | 7 | C5v, [5], (*55) | 10 | |||
33 | Pentagonal gyrokuppelrotunde | ![]() |
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25 | 50 | 27 | 15 | 5 | 7 | C5v, [5], (*55) | 10 | |||
34 | Pentagonal ortobirotunde | ![]() |
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30 | 60 | 32 | 20 | 12 | D5h, [5,2], (*225) | 20 | ||||
35 | Forlenget trekantet ortobikuppel | ![]() |
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18 | 36 | 20 | 8 | 12 | D3h, [3,2], (*223) | 12 | ||||
36 | Forlenget trekantet gyrobikuppel | ![]() |
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18 | 36 | 20 | 8 | 12 | D3d, [2+,6], (2*3) | 12 | ||||
37 | Forlenget kvadratisk gyrobikuppel | ![]() |
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24 | 48 | 26 | 8 | 18 | D4d, [2+,8], (2*4) | 16 | ||||
38 | Forlenget pentagonal ortobikuppel | ![]() |
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30 | 60 | 32 | 10 | 20 | 2 | D5h, [5,2], (*225) | 20 | |||
39 | Elongated pentagonal gyrobicupola | ![]() |
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30 | 60 | 32 | 10 | 20 | 2 | D5d, [2+,10], (2*5) | 20 | |||
40 | Elongated pentagonal orthocupolarotunda | ![]() |
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35 | 70 | 37 | 15 | 15 | 7 | C5v, [5], (*55) | 10 | |||
41 | Elongated pentagonal gyrocupolarotunda | ![]() |
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35 | 70 | 37 | 15 | 15 | 7 | C5v, [5], (*55) | 10 | |||
42 | Elongated pentagonal orthobirotunda | ![]() |
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40 | 80 | 42 | 20 | 10 | 12 | D5h, [5,2], (*225) | 20 | |||
43 | Elongated pentagonal gyrobirotunda | ![]() |
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40 | 80 | 42 | 20 | 10 | 12 | D5d, [2+,10], (2*5) | 20 | |||
44 | Gyroelongated triangular bicupola | ![]() |
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18 | 42 | 26 | 20 | 6 | D3, [3,2]+,(223) | 6 | ||||
45 | Gyroelongated square bicupola | ![]() |
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24 | 56 | 34 | 24 | 10 | D4, [4,2]+, (224) | 8 | ||||
46 | Gyroelongated pentagonal bicupola | ![]() |
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30 | 70 | 42 | 30 | 10 | 2 | D5, [5,2]+, (225) | 10 | |||
47 | Gyroelongated pentagonal cupolarotunda | ![]() |
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35 | 80 | 47 | 35 | 5 | 7 | C5, [5]+, (55) | 5 | |||
48 | Gyroelongated pentagonal birotunda | ![]() |
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40 | 90 | 52 | 40 | 12 | D5, [5,2]+, (225) | 10 | ||||
49 | Augmented triangular prism | ![]() |
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7 | 13 | 8 | 6 | 2 | C2v, [2], (*22) | 4 | ||||
50 | Biaugmented triangular prism | ![]() |
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8 | 17 | 11 | 10 | 1 | C2v, [2], (*22) | 4 | ||||
51 | Triaugmented triangular prism | ![]() |
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9 | 21 | 14 | 14 | D3h, [3,2], (*223) | 12 | |||||
52 | Augmented pentagonal prism | ![]() |
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11 | 19 | 10 | 4 | 4 | 2 | C2v, [2], (*22) | 4 | |||
53 | Biaugmented pentagonal prism | ![]() |
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12 | 23 | 13 | 8 | 3 | 2 | C2v, [2], (*22) | 4 | |||
54 | Augmented hexagonal prism | ![]() |
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13 | 22 | 11 | 4 | 5 | 2 | C2v, [2], (*22) | 4 | |||
55 | Parabiaugmented hexagonal prism | ![]() |
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14 | 26 | 14 | 8 | 4 | 2 | D2h, [2,2], (*222) | 8 | |||
56 | Metabiaugmented hexagonal prism | ![]() |
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14 | 26 | 14 | 8 | 4 | 2 | C2v, [2], (*22) | 4 | |||
57 | Triaugmented hexagonal prism | ![]() |
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15 | 30 | 17 | 12 | 3 | 2 | D3h, [3,2], (*223) | 12 | |||
58 | Augmented dodecahedron | ![]() |
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21 | 35 | 16 | 5 | 11 | C5v, [5], (*55) | 10 | ||||
59 | Parabiaugmented dodecahedron | ![]() |
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22 | 40 | 20 | 10 | 10 | D5d, [2+,10], (2*5) | 20 | ||||
60 | Metabiaugmented dodecahedron | ![]() |
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22 | 40 | 20 | 10 | 10 | C2v, [2], (*22) | 4 | ||||
61 | Triaugmented dodecahedron | ![]() |
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23 | 45 | 24 | 15 | 9 | C3v, [3], (*33) | 6 | ||||
62 | Metabidiminished icosahedron | ![]() |
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10 | 20 | 12 | 10 | 2 | C2v, [2], (*22) | 4 | ||||
63 | Tridiminished icosahedron | ![]() |
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9 | 15 | 8 | 5 | 3 | C3v, [3], (*33) | 6 | ||||
64 | Augmented tridiminished icosahedron | ![]() |
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10 | 18 | 10 | 7 | 3 | C3v, [3], (*33) | 6 | ||||
65 | Augmented truncated tetrahedron | ![]() |
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15 | 27 | 14 | 8 | 3 | 3 | C3v, [3], (*33) | 6 | |||
66 | Augmented truncated cube | ![]() |
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28 | 48 | 22 | 12 | 5 | 5 | C4v, [4], (*44) | 8 | |||
67 | Biaugmented truncated cube | ![]() |
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32 | 60 | 30 | 16 | 10 | 4 | D4h, [4,2], (*224) | 16 | |||
68 | Augmented truncated dodecahedron | ![]() |
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65 | 105 | 42 | 25 | 5 | 1 | 11 | C5v, [5], (*55) | 10 | ||
69 | Parabiaugmented truncated dodecahedron | ![]() |
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70 | 120 | 52 | 30 | 10 | 2 | 10 | D5d, [2+,10], (2*5) | 20 | ||
70 | Metabiaugmented truncated dodecahedron | ![]() |
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70 | 120 | 52 | 30 | 10 | 2 | 10 | C2v, [2], (*22) | 4 | ||
71 | Triaugmented truncated dodecahedron | ![]() |
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75 | 135 | 62 | 35 | 15 | 3 | 9 | C3v, [3], (*33) | 6 | ||
72 | Gyrate rhombicosidodecahedron | ![]() |
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60 | 120 | 62 | 20 | 30 | 12 | C5v, [5], (*55) | 10 | |||
73 | Parabigyrate rhombicosidodecahedron | ![]() |
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60 | 120 | 62 | 20 | 30 | 12 | D5d, [2+,10], (2*5) | 20 | |||
74 | Metabigyrate rhombicosidodecahedron | ![]() |
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60 | 120 | 62 | 20 | 30 | 12 | C2v, [2], (*22) | 4 | |||
75 | Trigyrate rhombicosidodecahedron | ![]() |
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60 | 120 | 62 | 20 | 30 | 12 | C3v, [3], (*33) | 6 | |||
76 | Diminished rhombicosidodecahedron | ![]() |
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55 | 105 | 52 | 15 | 25 | 11 | 1 | C5v, [5], (*55) | 10 | ||
77 | Paragyrate diminished rhombicosidodecahedron | ![]() |
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55 | 105 | 52 | 15 | 25 | 11 | 1 | C5v, [5], (*55) | 10 | ||
78 | Metagyrate diminished rhombicosidodecahedron | ![]() |
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55 | 105 | 52 | 15 | 25 | 11 | 1 | Cs, [ ], (*11) | 2 | ||
79 | Bigyrate diminished rhombicosidodecahedron | ![]() |
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55 | 105 | 52 | 15 | 25 | 11 | 1 | Cs, [ ], (*11) | 2 | ||
80 | Parabidiminished rhombicosidodecahedron | ![]() |
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50 | 90 | 42 | 10 | 20 | 10 | 2 | D5d, [2+,10], (2*5) | 20 | ||
81 | Metabidiminished rhombicosidodecahedron | ![]() |
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50 | 90 | 42 | 10 | 20 | 10 | 2 | C2v, [2], (*22) | 4 | ||
82 | Gyrate bidiminished rhombicosidodecahedron | ![]() |
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50 | 90 | 42 | 10 | 20 | 10 | 2 | Cs, [ ], (*11) | 2 | ||
83 | Tridiminished rhombicosidodecahedron | ![]() |
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45 | 75 | 32 | 5 | 15 | 9 | 3 | C3v, [3], (*33) | 6 | ||
84 | Snub disphenoid | ![]() |
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8 | 18 | 12 | 12 | D2d, [2+,4], (2*2) | 8 | |||||
85 | Snub square antiprism | ![]() |
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16 | 40 | 26 | 24 | 2 | D4d, [2+,8], (2*4) | 16 | ||||
86 | Sphenocorona | ![]() |
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10 | 22 | 14 | 12 | 2 | C2v, [2], (*22) | 4 | ||||
87 | Augmented sphenocorona | ![]() |
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11 | 26 | 17 | 16 | 1 | Cs, [ ], (*11) | 2 | ||||
88 | Sphenomegacorona | ![]() |
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12 | 28 | 18 | 16 | 2 | C2v, [2], (*22) | 4 | ||||
89 | Hebesphenomegacorona | ![]() |
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14 | 33 | 21 | 18 | 3 | C2v, [2], (*22) | 4 | ||||
90 | Disphenocingulum | ![]() |
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16 | 38 | 24 | 20 | 4 | D2d, [2+,4], (2*2) | 8 | ||||
91 | Bilunabirotunda | ![]() |
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14 | 26 | 14 | 8 | 2 | 4 | D2h, [2,2], (*222) | 8 | |||
92 | Triangular hebesphenorotunda | ![]() |
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18 | 36 | 20 | 13 | 3 | 3 | 1 | C3v, [3], (*33) | 6 |
Legend:
- Jn – Johnson Solid Number
- Net – Flattened (unfolded) image
- V – Number of Vertices
- E – Number of Edges
- F – Number of Faces (total)
- F3-F10 – Number of faces by side counts
References[rediger | rediger kilde]
- Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others.
- Victor A. Zalgaller (1969). Convex Polyhedra with Regular Faces. Consultants Bureau. No ISBN. The first proof that there are only 92 Johnson solids.
External links[rediger | rediger kilde]
- Sylvain Gagnon, "Convex polyhedra with regular faces", Structural Topology, No. 6, 1982, 83-95.
- Johnson Solids by George W. Hart.
- Images of all 92 solids, categorized, on one page
- (en) Eric W. Weisstein, Johnson Solid i MathWorld.
- VRML models of Johnson Solids by Jim McNeill
- VRML models of Johnson Solids by Vladimir Bulatov