Seznam Johnsonovih teles

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Johnsonovo telo je v geometriji strogo konveksni polieder, katerega je vsaka ploskev pravilni mnogokotnik, a ni uniformni, kot so recimo Platonsko telo, Arhimedsko telo, prizma ali antiprizma. Leta 1966 je Norman Johnson objavil seznam, ki je vključeval vseh 92 teles z navedenimi lastnostmi, dal jim je pa tudi imena in številke. Ni dokazal, da je 92 zares končno število. Leta 1969 je Victor Zalgaller dokazal, da je Johnsov seznam popoln.

Spodnja tabela je popolni seznam v stolpcih. Ostali poliedri se lahko konstruirajo tako, da imajo približno pravilne ploskve in se pogovorno imenujejo skoraj Johnsova telesa. V tem seznamu se jih ne upošteva.

Jn Ime telesa Mreža Slika O R P P3 P4 P5 P6 P8 P10 Simetrijska grupa Red
1 Kvadratna piramida Johnson solid 1 net.png Square pyramid.png 5 8 5 4 1 C4v, [4], (*44) 8
2 Petstrana piramida Johnson solid 2 net.png Pentagonal pyramid.png 6 10 6 5 1 C5v, [5], (*55) 10
3 Tristrana kupola Johnson solid 3 net.png Triangular cupola.png 9 15 8 4 3 1 C3v, [3], (*33) 6
4 Kvadratna kupola Johnson solid 4 net.png Square cupola.png 12 20 10 4 5 1 C4v, [4], (*44) 8
5 Petstrana kupola Johnson solid 5 net.png Pentagonal cupola.png 15 25 12 5 5 1 1 C5v, [5], (*55) 10
6 Pentagonal rotunda Johnson solid 6 net.png Pentagonal rotunda.png 20 35 17 10 6 1 C5v, [5], (*55) 10
7 Podaljšana tristrana piramida Johnson solid 7 net.png Elongated triangular pyramid.png 7 12 7 4 3 C3v, [3], (*33) 6
8 Podaljšana kvadratna piramida Johnson solid 8 net.png Elongated square pyramid.png 9 16 9 4 5 C4v, [4], (*44) 8
9 Podaljšana petstrana piramida Johnson solid 9 net.png Elongated pentagonal pyramid.png 11 20 11 5 5 1 C5v, [5], (*55) 10
10 Giro podaljšana kvadratna piramida Johnson solid 10 net.png Gyroelongated square pyramid.png 9 20 13 12 1 C4v, [4], (*44) 8
11 Giro podaljšana petstrana piramida Johnson solid 11 net.png Gyroelongated pentagonal pyramid.png 11 25 16 15 1 C5v, [5], (*55) 10
12 Tristrana bipiramida Johnson solid 12 net.png Triangular dipyramid.png 5 9 6 6 D3h, [3,2], (*223) 12
13 Petstrana bipiramida Johnson solid 13 net.png Pentagonal dipyramid.png 7 15 10 10 D5h, [5,2], (*225) 20
14 Podaljšana tristrana bipiramida Johnson solid 14 net.png Elongated triangular dipyramid.png 8 15 9 6 3 D3h, [3,2], (*223) 12
15 Podaljšana kvadratna bipiramida Johnson solid 15 net.png Elongated square dipyramid.png 10 20 12 8 4 D4h, [4,2], (*224) 16
16 Podaljšana petstrana bipiramida Johnson solid 16 net.png Elongated pentagonal dipyramid.png 12 25 15 10 5 D5h, [5,2], (*225) 20
17 Giro podaljšana kvadratna bipiramida Johnson solid 17 net.png Gyroelongated square dipyramid.png 10 24 16 16 D4d, [2+,8], (2*4) 16
18 Podaljšana tristrana kupola Johnson solid 18 net.png Elongated triangular cupola.png 15 27 14 4 9 1 C3v, [3], (*33) 6
19 Podaljšana kvadratna kupola Johnson solid 19 net.png Elongated square cupola.png 20 36 18 4 13 1 C4v, [4], (*44) 8
20 Podaljšana petstrana kupola Johnson solid 20 net.png Elongated pentagonal cupola.svg 25 45 22 5 15 1 1 C5v, [5], (*55) 10
21 Podaljšana petstrana rotunda Johnson solid 21 net.png Elongated pentagonal rotunda.png 30 55 27 10 10 6 1 C5v, [5], (*55) 10
22 Giro podaljšana tristrana kupola Johnson solid 22 net.png Gyroelongated triangular cupola.png 15 33 20 16 3 1 C3v, [3], (*33) 6
23 Giro podaljšana kvadratna kupola Johnson solid 23 net.png Gyroelongated square cupola.png 20 44 26 20 5 1 C4v, [4], (*44) 8
24 Giro podaljšana petstrana kupola Johnson solid 24 net.png Gyroelongated pentagonal cupola.png 25 55 32 25 5 1 1 C5v, [5], (*55) 10
25 Giro podaljšana petstrana rotunda Johnson solid 25 net.png Gyroelongated pentagonal rotunda.png 30 65 37 30 6 1 C5v, [5], (*55) 10
26 Girobifastigij Johnson solid 26 net.png Gyrobifastigium.png 8 14 8 4 4 D2d, [2+,4], (2*2) 8
27 Tristrana ortobikupola Johnson solid 27 net.png Triangular orthobicupola.png 12 24 14 8 6 D3h, [3,2], (*223) 12
28 Kvadratna ortobikupola Johnson solid 28 net.png Square orthobicupola.png 16 32 18 8 10 D4h, [4,2], (*224) 16
29 Kvadratna girobikupola Johnson solid 29 net.png Square gyrobicupola.png 16 32 18 8 10 D4d, [2+,8], (2*4) 16
30 Petstrana ortobikupola Johnson solid 30 net.png Pentagonal orthobicupola.png 20 40 22 10 10 2 D5h, [5,2], (*225) 20
31 Petstrana girobikupola Johnson solid 31 net.png Pentagonal gyrobicupola.png 20 40 22 10 10 2 D5d, [2+,10], (2*5) 20
32 Petstrana ortokupolarotunda Johnson solid 32 net.png Pentagonal orthocupolarotunda.png 25 50 27 15 5 7 C5v, [5], (*55) 10
33 Petstrana girokupolarotunda Johnson solid 33 net.png Pentagonal gyrocupolarotunda.png 25 50 27 15 5 7 C5v, [5], (*55) 10
34 Petstrana ortobirotunda Johnson solid 34 net.png Pentagonal orthobirotunda.png 30 60 32 20 12 D5h, [5,2], (*225) 20
35 Podaljšana tristrana ortobikupola Johnson solid 35 net.png Elongated triangular orthobicupola.png 18 36 20 8 12 D3h, [3,2], (*223) 12
36 Podaljšana tristrana girobikupola Johnson solid 36 net.png Elongated triangular gyrobicupola.png 18 36 20 8 12 D3d, [2+,6], (2*3) 12
37 Podaljšana kvadratna girobikupola Johnson solid 37 net.png Elongated square gyrobicupola.png 24 48 26 8 18 D4d, [2+,8], (2*4) 16
38 Podaljšana petstrana ortobikupola Johnson solid 38 net.png Elongated pentagonal orthobicupola.png 30 60 32 10 20 2 D5h, [5,2], (*225) 20
39 Podaljšana petstrana girobikupola Johnson solid 39 net.png Elongated pentagonal gyrobicupola.png 30 60 32 10 20 2 D5d, [2+,10], (2*5) 20
40 Podaljšana petstrana ortokupolarotunda Johnson solid 40 net.png Elongated pentagonal orthocupolarotunda.png 35 70 37 15 15 7 C5v, [5], (*55) 10
41 Podaljšana petstrana girokupolarotunda Johnson solid 41 net.png Elongated pentagonal gyrocupolarotunda.png 35 70 37 15 15 7 C5v, [5], (*55) 10
42 Podaljšana petstrana ortobirotunda Johnson solid 42 net.png Elongated pentagonal orthobirotunda.png 40 80 42 20 10 12 D5h, [5,2], (*225) 20
43 Podaljšana petstrana girobirotunda Johnson solid 43 net.png Elongated pentagonal gyrobirotunda.png 40 80 42 20 10 12 D5d, [2+,10], (2*5) 20
44 Giro podaljšana tristrana bikupola Johnson solid 44 net.png Gyroelongated triangular bicupola.png 18 42 26 20 6 D3, [3,2]+,(223) 6
45 Giro podaljšana kvadratna bikupola Johnson solid 45 net.png Gyroelongated square bicupola.png 24 56 34 24 10 D4, [4,2]+, (224) 8
46 Giro podaljšana petstrana bikupola Johnson solid 46 net.png Gyroelongated pentagonal bicupola.png 30 70 42 30 10 2 D5, [5,2]+, (225) 10
47 Giro podaljšana petstrana kupolarotunda Johnson solid 47 net.png Gyroelongated pentagonal cupolarotunda.png 35 80 47 35 5 7 C5, [5]+, (55) 5
48 Giro podaljšana petstrana birotunda Johnson solid 48 net.png Gyroelongated pentagonal birotunda.png 40 90 52 40 12 D5, [5,2]+, (225) 10
49 Povečana tristrana prizma Johnson solid 49 net.png Augmented triangular prism.png 7 13 8 6 2 C2v, [2], (*22) 4
50 Dvojno povečana tristrana prizma Johnson solid 50 net.png Biaugmented triangular prism.png 8 17 11 10 1 C2v, [2], (*22) 4
51 Trojno povečana tristrana prizma Johnson solid 51 net.png Triaugmented triangular prism.png 9 21 14 14 D3h, [3,2], (*223) 12
52 Povečana petstrana prizma Johnson solid 52 net.png Augmented pentagonal prism.png 11 19 10 4 4 2 C2v, [2], (*22) 4
53 Dvojno povečana petstrana prizma Johnson solid 53 net.png Biaugmented pentagonal prism.png 12 23 13 8 3 2 C2v, [2], (*22) 4
54 Povečana šeststrana prizma Johnson solid 54 net.png Augmented hexagonal prism.png 13 22 11 4 5 2 C2v, [2], (*22) 4
55 Para dvojno povečana šeststrana prizma Johnson solid 55 net.png Parabiaugmented hexagonal prism.png 14 26 14 8 4 2 D2h, [2,2], (*222) 8
56 Meta dvojno povečana šeststrana prizma Johnson solid 56 net.png Metabiaugmented hexagonal prism.png 14 26 14 8 4 2 C2v, [2], (*22) 4
57 Trojno povečana šeststrana prizma Johnson solid 57 net.png Triaugmented hexagonal prism.png 15 30 17 12 3 2 D3h, [3,2], (*223) 12
58 Povečan dodekaeder Johnson solid 58 net.png Augmented dodecahedron.png 21 35 16 5 11 C5v, [5], (*55) 10
59 Para dvojno povečan dodekaeder Johnson solid 59 net.png Parabiaugmented dodecahedron.png 22 40 20 10 10 D5d, [2+,10], (2*5) 20
60 Meta dvojno povečan dodekaeder Johnson solid 60 net.png Metabiaugmented dodecahedron.png 22 40 20 10 10 C2v, [2], (*22) 4
61 Trojno povečan dodekaeder Johnson solid 61 net.png Triaugmented dodecahedron.png 23 45 24 15 9 C3v, [3], (*33) 6
62 Meta dvojno izginjajoč ikozaeder Johnson solid 62 net.png Metabidiminished icosahedron.png 10 20 12 10 2 C2v, [2], (*22) 4
63 Trojno izginjajoč ikozaeder Johnson solid 63 net.png Tridiminished icosahedron.png 9 15 8 5 3 C3v, [3], (*33) 6
64 Povečan trojno izginjajoč ikozaeder Johnson solid 64 net.png Augmented tridiminished icosahedron.png 10 18 10 7 3 C3v, [3], (*33) 6
65 Povečan prisekan tetraeder Johnson solid 65 net.png Augmented truncated tetrahedron.png 15 27 14 8 3 3 C3v, [3], (*33) 6
66 Povečana prisekana kocka Johnson solid 66 net.png Augmented truncated cube.png 28 48 22 12 5 5 C4v, [4], (*44) 8
67 Dvojno povečana prisekana kocka Johnson solid 67 net.png Biaugmented truncated cube.png 32 60 30 16 10 4 D4h, [4,2], (*224) 16
68 Povečan prisekan dodekaeder Johnson solid 68 net.png Augmented truncated dodecahedron.png 65 105 42 25 5 1 11 C5v, [5], (*55) 10
69 Para dvojno povečan prisekan dodekaeder Johnson solid 69 net.png Parabiaugmented truncated dodecahedron.png 70 120 52 30 10 2 10 D5d, [2+,10], (2*5) 20
70 Meta dvojno povečan prisekan dodekaeder Johnson solid 70 net.png Metabiaugmented truncated dodecahedron.png 70 120 52 30 10 2 10 C2v, [2], (*22) 4
71 Trojno povečan prisekan dodekaeder Johnson solid 71 net.png Triaugmented truncated dodecahedron.png 75 135 62 35 15 3 9 C3v, [3], (*33) 6
72 Girorombiikozidodekaeder Johnson solid 72 net.png Gyrate rhombicosidodecahedron.png 60 120 62 20 30 12 C5v, [5], (*55) 10
73 Para dvojni girorombiikozidodekaeder Johnson solid 73 net.png Parabigyrate rhombicosidodecahedron.png 60 120 62 20 30 12 D5d, [2+,10], (2*5) 20
74 Meta dvojni girorombiikozidodekaeder Johnson solid 74 net.png Metabigyrate rhombicosidodecahedron.png 60 120 62 20 30 12 C2v, [2], (*22) 4
75 Trojni girorombiikozidodekaeder Johnson solid 75 net.png Trigyrate rhombicosidodecahedron.png 60 120 62 20 30 12 C3v, [3], (*33) 6
76 Izginjajoč rombiikozidodekaeder Johnson solid 76 net.png Diminished rhombicosidodecahedron.png 55 105 52 15 25 11 1 C5v, [5], (*55) 10
77 Para giro izginjajoč rombiikozidodekaeder Johnson solid 77 net.png Paragyrate diminished rhombicosidodecahedron.png 55 105 52 15 25 11 1 C5v, [5], (*55) 10
78 Meta giro izginjajoč rombiikozidodekaeder Johnson solid 78 net.png Metagyrate diminished rhombicosidodecahedron.png 55 105 52 15 25 11 1 Cs, [ ], (*11) 2
79 Dvojno giro izginjajoči rombiikozidodekaeder Johnson solid 79 net.png Bigyrate diminished rhombicosidodecahedron.png 55 105 52 15 25 11 1 Cs, [ ], (*11) 2
80 Para dvojno izginjajoč rombiikozidodekaeder Johnson solid 80 net.png Parabidiminished rhombicosidodecahedron.png 50 90 42 10 20 10 2 D5d, [2+,10], (2*5) 20
81 Meta dvojno izginjajoč rombiikozidodekaeder Johnson solid 81 net.png Metabidiminished rhombicosidodecahedron.png 50 90 42 10 20 10 2 C2v, [2], (*22) 4
82 Giro dvojno izginjajoč rombiikozidodekaeder Johnson solid 82 net.png Gyrate bidiminished rhombicosidodecahedron.png 50 90 42 10 20 10 2 Cs, [ ], (*11) 2
83 Trojno izginjajoč rombiikozidodekaeder Johnson solid 83 net.png Tridiminished rhombicosidodecahedron.png 45 75 32 5 15 9 3 C3v, [3], (*33) 6
84 Prirezani disfenoid Johnson solid 84 net.png Snub disphenoid.png 8 18 12 12 D2d, [2+,4], (2*2) 8
85 Prirezana kvadratna antiprizma Johnson solid 85 net.png Snub square antiprism.png 16 40 26 24 2 D4d, [2+,8], (2*4) 16
86 Sfenokorona Johnson solid 86 net.png Sphenocorona.png 10 22 14 12 2 C2v, [2], (*22) 4
87 Povečana sfenokorona Johnson solid 87 net.png Augmented sphenocorona.png 11 26 17 16 1 Cs, [ ], (*11) 2
88 Sfenomegakorona Johnson solid 88 net.png Sphenomegacorona.png 12 28 18 16 2 C2v, [2], (*22) 4
89 Hebesfenomegakorona Johnson solid 89 net.png Hebesphenomegacorona.png 14 33 21 18 3 C2v, [2], (*22) 4
90 Disfenocingul Johnson solid 90 net.png Disphenocingulum.png 16 38 24 20 4 D2d, [2+,4], (2*2) 8
91 Dvojna lunabirotunda Johnson solid 91 net.png Bilunabirotunda.png 14 26 14 8 2 4 D2h, [2,2], (*222) 8
92 Tristrana hebesfenorotunda Johnson solid 92 net.png Triangular hebesphenorotunda.png 18 36 20 13 3 3 1 C3v, [3], (*33) 6
na vrh WWC arrow up.png

Legenda:

  • Jn – Številka Johnsovega telesa
  • Mreža – Sploščena (neprepognjena) slika
  • O – Število oglišč
  • R – Število robov
  • P – Skupno število ploskev
  • P3-P10 – Število ploskev (šteto od strani)

Sklici[uredi | uredi kodo]

  • 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.

Zunanje povezave[uredi | uredi kodo]