Gebruiker:Patrick/johnsonlichamen

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Een johnsonlichaam is een convex veelvlak waarvan elk zijvlak een regelmatige veelhoek is, en dat niet een regelmatig veelvlak (platonisch lichaam), archimedisch lichaam, prisma of antiprisma is.

Het is niet verplicht dat elk zijvlak uit eenzelfde type veelhoek moet bestaan of dat steeds de dezelfde configuratie van veelhoeken samenkomt in de hoekpunten. Een voorbeeld van een Johnson-lichaam is een vierkante piramide met gelijke zijden (J1). Het heeft een vierkante basis en vier driehoekige zijvlakken.

De zijvlakken van johnsonlichamen hebben allemaal 3, 4, 5, 6, 8 of 10 zijden.

Engels[bewerken | brontekst bewerken]

en:List of Johnson solids

In geometry, a Johnson solid is a strictly convex polyhedron, each face of which is a regular polygon, but which is not uniform, i.e., not a Platonic solid, Archimedean solid, prism or antiprism. In 1966, Norman Johnson published a list which included all 92 solids, and gave them their names and numbers. He did not prove that there were only 92, but he did conjecture that there were no others. Victor Zalgaller in 1969 proved that Johnson's list was complete.

The complete list is here with sorting by column. Other polyhedra can be constructed that are only approximately regular planar polygon faces, and are informally called near-miss Johnson solid; there can be no definitive count of them.

Jn Solid name Net Image H R Z Z3 Z4 Z5 Z6 Z8 Z10 Symmetrie orde
1 Square pyramid Johnson solid 1 net.png Square pyramid.png 5 8 5 4 1 C4v, [4], (*44) 8
2 Pentagonal pyramid Johnson solid 2 net.png Pentagonal pyramid.png 6 10 6 5 1 C5v, [5], (*55) 10
3 Triangular cupola Johnson solid 3 net.png Triangular cupola.png 9 15 8 4 3 1 C3v, [3], (*33) 6
4 Square cupola Johnson solid 4 net.png Square cupola.png 12 20 10 4 5 1 C4v, [4], (*44) 8
5 Pentagonal cupola 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 Elongated triangular pyramid Johnson solid 7 net.png Elongated triangular pyramid.png 7 12 7 4 3 C3v, [3], (*33) 6
8 Elongated square pyramid Johnson solid 8 net.png Elongated square pyramid.png 9 16 9 4 5 C4v, [4], (*44) 8
9 Elongated pentagonal pyramid Johnson solid 9 net.png Elongated pentagonal pyramid.png 11 20 11 5 5 1 C5v, [5], (*55) 10
10 Gyroelongated square pyramid Johnson solid 10 net.png Gyroelongated square pyramid.png 9 20 13 12 1 C4v, [4], (*44) 8
11 Gyroelongated pentagonal pyramid Johnson solid 11 net.png Gyroelongated pentagonal pyramid.png 11 25 16 15 1 C5v, [5], (*55) 10
12 Triangular bipyramid Johnson solid 12 net.png Triangular dipyramid.png 5 9 6 6 D3h, [3,2], (*223) 12
13 Pentagonal bipyramid Johnson solid 13 net.png Pentagonal dipyramid.png 7 15 10 10 D5h, [5,2], (*225) 20
14 Elongated triangular bipyramid Johnson solid 14 net.png Elongated triangular dipyramid.png 8 15 9 6 3 D3h, [3,2], (*223) 12
15 Elongated square bipyramid Johnson solid 15 net.png Elongated square dipyramid.png 10 20 12 8 4 D4h, [4,2], (*224) 16
16 Elongated pentagonal bipyramid Johnson solid 16 net.png Elongated pentagonal dipyramid.png 12 25 15 10 5 D5h, [5,2], (*225) 20
17 Gyroelongated square bipyramid Johnson solid 17 net.png Gyroelongated square dipyramid.png 10 24 16 16 D4d, [2+,8], (2*4) 16
18 Elongated triangular cupola Johnson solid 18 net.png Elongated triangular cupola.png 15 27 14 4 9 1 C3v, [3], (*33) 6
19 Elongated square cupola Johnson solid 19 net.png Elongated square cupola.png 20 36 18 4 13 1 C4v, [4], (*44) 8
20 Elongated pentagonal cupola Johnson solid 20 net.png Elongated pentagonal cupola.svg 25 45 22 5 15 1 1 C5v, [5], (*55) 10
21 Elongated pentagonal rotunda Johnson solid 21 net.png Elongated pentagonal rotunda.png 30 55 27 10 10 6 1 C5v, [5], (*55) 10
22 Gyroelongated triangular cupola Johnson solid 22 net.png Gyroelongated triangular cupola.png 15 33 20 16 3 1 C3v, [3], (*33) 6
23 Gyroelongated square cupola Johnson solid 23 net.png Gyroelongated square cupola.png 20 44 26 20 5 1 C4v, [4], (*44) 8
24 Gyroelongated pentagonal cupola Johnson solid 24 net.png Gyroelongated pentagonal cupola.png 25 55 32 25 5 1 1 C5v, [5], (*55) 10
25 Gyroelongated pentagonal rotunda Johnson solid 25 net.png Gyroelongated pentagonal rotunda.png 30 65 37 30 6 1 C5v, [5], (*55) 10
26 Gyrobifastigium Johnson solid 26 net.png Gyrobifastigium.png 8 14 8 4 4 D2d, [2+,4], (2*2) 8
27 Triangular orthobicupola Johnson solid 27 net.png Triangular orthobicupola.png 12 24 14 8 6 D3h, [3,2], (*223) 12
28 Square orthobicupola Johnson solid 28 net.png Square orthobicupola.png 16 32 18 8 10 D4h, [4,2], (*224) 16
29 Square gyrobicupola Johnson solid 29 net.png Square gyrobicupola.png 16 32 18 8 10 D4d, [2+,8], (2*4) 16
30 Pentagonal orthobicupola Johnson solid 30 net.png Pentagonal orthobicupola.png 20 40 22 10 10 2 D5h, [5,2], (*225) 20
31 Pentagonal gyrobicupola Johnson solid 31 net.png Pentagonal gyrobicupola.png 20 40 22 10 10 2 D5d, [2+,10], (2*5) 20
32 Pentagonal orthocupolarotunda Johnson solid 32 net.png Pentagonal orthocupolarotunda.png 25 50 27 15 5 7 C5v, [5], (*55) 10
33 Pentagonal gyrocupolarotunda Johnson solid 33 net.png Pentagonal gyrocupolarotunda.png 25 50 27 15 5 7 C5v, [5], (*55) 10
34 Pentagonal orthobirotunda Johnson solid 34 net.png Pentagonal orthobirotunda.png 30 60 32 20 12 D5h, [5,2], (*225) 20
35 Elongated triangular orthobicupola Johnson solid 35 net.png Elongated triangular orthobicupola.png 18 36 20 8 12 D3h, [3,2], (*223) 12
36 Elongated triangular gyrobicupola Johnson solid 36 net.png Elongated triangular gyrobicupola.png 18 36 20 8 12 D3d, [2+,6], (2*3) 12
37 Elongated square gyrobicupola Johnson solid 37 net.png Elongated square gyrobicupola.png 24 48 26 8 18 D4d, [2+,8], (2*4) 16
38 Elongated pentagonal orthobicupola Johnson solid 38 net.png Elongated pentagonal orthobicupola.png 30 60 32 10 20 2 D5h, [5,2], (*225) 20
39 Elongated pentagonal gyrobicupola Johnson solid 39 net.png Elongated pentagonal gyrobicupola.png 30 60 32 10 20 2 D5d, [2+,10], (2*5) 20
40 Elongated pentagonal orthocupolarotunda Johnson solid 40 net.png Elongated pentagonal orthocupolarotunda.png 35 70 37 15 15 7 C5v, [5], (*55) 10
41 Elongated pentagonal gyrocupolarotunda Johnson solid 41 net.png Elongated pentagonal gyrocupolarotunda.png 35 70 37 15 15 7 C5v, [5], (*55) 10
42 Elongated pentagonal orthobirotunda Johnson solid 42 net.png Elongated pentagonal orthobirotunda.png 40 80 42 20 10 12 D5h, [5,2], (*225) 20
43 Elongated pentagonal gyrobirotunda Johnson solid 43 net.png Elongated pentagonal gyrobirotunda.png 40 80 42 20 10 12 D5d, [2+,10], (2*5) 20
44 Gyroelongated triangular bicupola Johnson solid 44 net.png Gyroelongated triangular bicupola.png 18 42 26 20 6 D3, [3,2]+,(223) 6
45 Gyroelongated square bicupola Johnson solid 45 net.png Gyroelongated square bicupola.png 24 56 34 24 10 D4, [4,2]+, (224) 8
46 Gyroelongated pentagonal bicupola Johnson solid 46 net.png Gyroelongated pentagonal bicupola.png 30 70 42 30 10 2 D5, [5,2]+, (225) 10
47 Gyroelongated pentagonal cupolarotunda Johnson solid 47 net.png Gyroelongated pentagonal cupolarotunda.png 35 80 47 35 5 7 C5, [5]+, (55) 5
48 Gyroelongated pentagonal birotunda Johnson solid 48 net.png Gyroelongated pentagonal birotunda.png 40 90 52 40 12 D5, [5,2]+, (225) 10
49 Augmented triangular prism Johnson solid 49 net.png Augmented triangular prism.png 7 13 8 6 2 C2v, [2], (*22) 4
50 Biaugmented triangular prism Johnson solid 50 net.png Biaugmented triangular prism.png 8 17 11 10 1 C2v, [2], (*22) 4
51 Triaugmented triangular prism Johnson solid 51 net.png Triaugmented triangular prism.png 9 21 14 14 D3h, [3,2], (*223) 12
52 Augmented pentagonal prism Johnson solid 52 net.png Augmented pentagonal prism.png 11 19 10 4 4 2 C2v, [2], (*22) 4
53 Biaugmented pentagonal prism Johnson solid 53 net.png Biaugmented pentagonal prism.png 12 23 13 8 3 2 C2v, [2], (*22) 4
54 Augmented hexagonal prism Johnson solid 54 net.png Augmented hexagonal prism.png 13 22 11 4 5 2 C2v, [2], (*22) 4
55 Parabiaugmented hexagonal prism Johnson solid 55 net.png Parabiaugmented hexagonal prism.png 14 26 14 8 4 2 D2h, [2,2], (*222) 8
56 Metabiaugmented hexagonal prism Johnson solid 56 net.png Metabiaugmented hexagonal prism.png 14 26 14 8 4 2 C2v, [2], (*22) 4
57 Triaugmented hexagonal prism Johnson solid 57 net.png Triaugmented hexagonal prism.png 15 30 17 12 3 2 D3h, [3,2], (*223) 12
58 Augmented dodecahedron Johnson solid 58 net.png Augmented dodecahedron.png 21 35 16 5 11 C5v, [5], (*55) 10
59 Parabiaugmented dodecahedron Johnson solid 59 net.png Parabiaugmented dodecahedron.png 22 40 20 10 10 D5d, [2+,10], (2*5) 20
60 Metabiaugmented dodecahedron Johnson solid 60 net.png Metabiaugmented dodecahedron.png 22 40 20 10 10 C2v, [2], (*22) 4
61 Triaugmented dodecahedron Johnson solid 61 net.png Triaugmented dodecahedron.png 23 45 24 15 9 C3v, [3], (*33) 6
62 Metabidiminished icosahedron Johnson solid 62 net.png Metabidiminished icosahedron.png 10 20 12 10 2 C2v, [2], (*22) 4
63 Tridiminished icosahedron Johnson solid 63 net.png Tridiminished icosahedron.png 9 15 8 5 3 C3v, [3], (*33) 6
64 Augmented tridiminished icosahedron Johnson solid 64 net.png Augmented tridiminished icosahedron.png 10 18 10 7 3 C3v, [3], (*33) 6
65 Augmented truncated tetrahedron Johnson solid 65 net.png Augmented truncated tetrahedron.png 15 27 14 8 3 3 C3v, [3], (*33) 6
66 Augmented truncated cube Johnson solid 66 net.png Augmented truncated cube.png 28 48 22 12 5 5 C4v, [4], (*44) 8
67 Biaugmented truncated cube Johnson solid 67 net.png Biaugmented truncated cube.png 32 60 30 16 10 4 D4h, [4,2], (*224) 16
68 Augmented truncated dodecahedron Johnson solid 68 net.png Augmented truncated dodecahedron.png 65 105 42 25 5 1 11 C5v, [5], (*55) 10
69 Parabiaugmented truncated dodecahedron Johnson solid 69 net.png Parabiaugmented truncated dodecahedron.png 70 120 52 30 10 2 10 D5d, [2+,10], (2*5) 20
70 Metabiaugmented truncated dodecahedron Johnson solid 70 net.png Metabiaugmented truncated dodecahedron.png 70 120 52 30 10 2 10 C2v, [2], (*22) 4
71 Triaugmented truncated dodecahedron Johnson solid 71 net.png Triaugmented truncated dodecahedron.png 75 135 62 35 15 3 9 C3v, [3], (*33) 6
72 Gyrate rhombicosidodecahedron Johnson solid 72 net.png Gyrate rhombicosidodecahedron.png 60 120 62 20 30 12 C5v, [5], (*55) 10
73 Parabigyrate rhombicosidodecahedron Johnson solid 73 net.png Parabigyrate rhombicosidodecahedron.png 60 120 62 20 30 12 D5d, [2+,10], (2*5) 20
74 Metabigyrate rhombicosidodecahedron Johnson solid 74 net.png Metabigyrate rhombicosidodecahedron.png 60 120 62 20 30 12 C2v, [2], (*22) 4
75 Trigyrate rhombicosidodecahedron Johnson solid 75 net.png Trigyrate rhombicosidodecahedron.png 60 120 62 20 30 12 C3v, [3], (*33) 6
76 Diminished rhombicosidodecahedron Johnson solid 76 net.png Diminished rhombicosidodecahedron.png 55 105 52 15 25 11 1 C5v, [5], (*55) 10
77 Paragyrate diminished rhombicosidodecahedron Johnson solid 77 net.png Paragyrate diminished rhombicosidodecahedron.png 55 105 52 15 25 11 1 C5v, [5], (*55) 10
78 Metagyrate diminished rhombicosidodecahedron Johnson solid 78 net.png Metagyrate diminished rhombicosidodecahedron.png 55 105 52 15 25 11 1 Cs, [ ], (*11) 2
79 Bigyrate diminished rhombicosidodecahedron Johnson solid 79 net.png Bigyrate diminished rhombicosidodecahedron.png 55 105 52 15 25 11 1 Cs, [ ], (*11) 2
80 Parabidiminished rhombicosidodecahedron Johnson solid 80 net.png Parabidiminished rhombicosidodecahedron.png 50 90 42 10 20 10 2 D5d, [2+,10], (2*5) 20
81 Metabidiminished rhombicosidodecahedron Johnson solid 81 net.png Metabidiminished rhombicosidodecahedron.png 50 90 42 10 20 10 2 C2v, [2], (*22) 4
82 Gyrate bidiminished rhombicosidodecahedron Johnson solid 82 net.png Gyrate bidiminished rhombicosidodecahedron.png 50 90 42 10 20 10 2 Cs, [ ], (*11) 2
83 Tridiminished rhombicosidodecahedron Johnson solid 83 net.png Tridiminished rhombicosidodecahedron.png 45 75 32 5 15 9 3 C3v, [3], (*33) 6
84 Snub disphenoid Johnson solid 84 net.png Snub disphenoid.png 8 18 12 12 D2d, [2+,4], (2*2) 8
85 Snub square antiprism Johnson solid 85 net.png Snub square antiprism.png 16 40 26 24 2 D4d, [2+,8], (2*4) 16
86 Sphenocorona Johnson solid 86 net.png Sphenocorona.png 10 22 14 12 2 C2v, [2], (*22) 4
87 Augmented sphenocorona Johnson solid 87 net.png Augmented sphenocorona.png 11 26 17 16 1 Cs, [ ], (*11) 2
88 Sphenomegacorona Johnson solid 88 net.png Sphenomegacorona.png 12 28 18 16 2 C2v, [2], (*22) 4
89 Hebesphenomegacorona Johnson solid 89 net.png Hebesphenomegacorona.png 14 33 21 18 3 C2v, [2], (*22) 4
90 Disphenocingulum Johnson solid 90 net.png Disphenocingulum.png 16 38 24 20 4 D2d, [2+,4], (2*2) 8
91 Bilunabirotunda Johnson solid 91 net.png Bilunabirotunda.png 14 26 14 8 2 4 D2h, [2,2], (*222) 8
92 Triangular hebesphenorotunda Johnson solid 92 net.png Triangular hebesphenorotunda.png 18 36 20 13 3 3 1 C3v, [3], (*33) 6

Sjabloon:Right 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

Nederlands[bewerken | brontekst bewerken]

Hieronder volgt de lijst van johnsonlichamen, maar sorteerbaar, zie daar voor de indeling.

  • 1 Piramiden, prismatoïden en rotonden
  • 2 Getransformeerde piramiden en bipiramiden
  • 3 Getransformeerde koepels en rotonden
  • 4 Verhoogde prisma's
  • 5 Getransformeerde platonische lichamen
  • 6 Getransformeerde archimedische lichamen
  • 7 Overige lichamen
Jn Naam Openvouwing Afbeelding Symmetriegroep
1 Vierkante piramide Johnson solid 1 net.png Square pyramid.png C4v
2 Vijfhoekige piramide Johnson solid 2 net.png Pentagonal pyramid.png C5v
3 Driehoekige koepel Johnson solid 3 net.png Triangular cupola.png C3v
4 Vierkante koepel Johnson solid 4 net.png Square cupola.png C4v
5 Vijfhoekige koepel Johnson solid 5 net.png Pentagonal cupola.png C5v
6 Vijfhoekige rotonde Johnson solid 6 net.png Pentagonal rotunda.png C5v
7 Verlengde driehoekige piramide Johnson solid 7 net.png Elongated triangular pyramid.png C3v
8 Verlengde vierkante piramide Johnson solid 8 net.png Elongated square pyramid.png C4v
9 Verlengde vijfhoekige piramide Johnson solid 9 net.png Elongated pentagonal pyramid.png C5v
10 Verlengde gedraaide vierkante piramide Johnson solid 10 net.png Gyroelongated square pyramid.png C4v
11 Verlengde gedraaide vijfhoekige piramide Johnson solid 11 net.png Gyroelongated pentagonal pyramid.png C5v
12 Driehoekige bipiramide Johnson solid 12 net.png Triangular dipyramid.png D3h
13 Vijfhoekige bipiramide Johnson solid 13 net.png Pentagonal dipyramid.png D5h
14 Verlengde driehoekige bipiramide Johnson solid 14 net.png Elongated triangular dipyramid.png D3h
15 Verlengde vierkante bipiramide Johnson solid 15 net.png Elongated square dipyramid.png D4h
16 Verlengde vijfhoekige bipiramide Johnson solid 16 net.png Elongated pentagonal dipyramid.png D5h
17 Verlengde gedraaide vierkante bipiramide Johnson solid 17 net.png Gyroelongated square dipyramid.png D4d
18 Verlengde driehoekige koepel Johnson solid 18 net.png Elongated triangular cupola.png C3v
19 Verlengde vierkante koepel Johnson solid 19 net.png Elongated square cupola.png C4v
20 Verlengde vijfhoekige koepel Johnson solid 20 net.png Elongated pentagonal cupola.png C5v
21 Verlengde vijfhoekige rotonde Johnson solid 21 net.png Elongated pentagonal rotunda.png C5v
22 Verlengde gedraaide driehoekige koepel Johnson solid 22 net.png Gyroelongated triangular cupola.png C3v
23 Verlengde gedraaide vierkante koepel Johnson solid 23 net.png Gyroelongated square cupola.png C4v
24 Verlengde gedraaide vijfhoekige koepel Johnson solid 24 net.png Gyroelongated pentagonal cupola.png C5v
25 Verlengde gedraaide vijfhoekige rotonde Johnson solid 25 net.png Gyroelongated pentagonal rotunda.png C5v
26 Gyrobifastigium Johnson solid 26 net.png Gyrobifastigium.png D2d
27 Gedraaide kuboctaëder Johnson solid 27 net.png Triangular orthobicupola.png D3h
28 Vierkante orthogonale dubbelkoepel Johnson solid 28 net.png Square orthobicupola.png D4h
29 Gedraaide vierkante dubbelkoepel Johnson solid 29 net.png Square gyrobicupola.png D4d
30 Vijfhoekige orthogonale dubbelkoepel Johnson solid 30 net.png Pentagonal orthobicupola.png D5h
31 Gedraaide vijfhoekige dubbelkoepel Johnson solid 31 net.png Pentagonal gyrobicupola.png D5d
32 Vijfhoekige orthogonale koepelrotonde Johnson solid 32 net.png Pentagonal orthocupolarotunda.png C5v
33 Vijfhoekige gedraaide koepelrotonde Johnson solid 33 net.png Pentagonal gyrocupolarotunda.png C5v
34 Gedraaide icosidodecaëder Johnson solid 34 net.png Pentagonal orthobirotunda.png D5h
35 Verlengde driehoekige orthogonale dubbelkoepel Johnson solid 35 net.png Elongated triangular orthobicupola.png D3h
36 Verlengde gedraaide driehoekige dubbelkoepel Johnson solid 36 net.png Elongated triangular gyrobicupola.png D3d
37 Gedraaide romboëdrisch kuboctaëder
(=Verlengde gedraaide dubbelkoepel)
Johnson solid 37 net.png Elongated square gyrobicupola.png D4d
38 Verlengde vijfhoekige orthogonale dubbelkoepel Johnson solid 38 net.png Elongated pentagonal orthobicupola.png D5h
39 Verlengde gedraaide vijfhoekige dubbelkoepel Johnson solid 39 net.png Elongated pentagonal gyrobicupola.png D5d
40 Verlengde vijfhoekige orthogonale koepelrotonde Johnson solid 40 net.png Elongated pentagonal orthocupolarotunda.png C5v
41 Verlengde gedraaide vijfhoekige koepelrotonde Johnson solid 41 net.png Elongated pentagonal gyrocupolarotunda.png C5v
42 Verlengde vijfhoekige orthogonale dubbelrotonde Johnson solid 42 net.png Elongated pentagonal orthobirotunda.png D5h
43 Verlengde gedraaide vijfhoekige dubbelrotonde Johnson solid 43 net.png Elongated pentagonal gyrobirotunda.png D5d
44 Verlengde dubbelgedraaide driehoekige dubbelkoepel Johnson solid 44 net.png Gyroelongated triangular bicupola.png D3
45 Verlengde gedraaide vierkante dubbelkoepel Johnson solid 45 net.png Gyroelongated square bicupola.png D4
46 Verlengde dubbelgedraaide vijfhoekige dubbelkoepel Johnson solid 46 net.png Gyroelongated pentagonal bicupola.png D5
47 Verlengde dubbelgedraaide vijfhoekige koepelrotonde Johnson solid 47 net.png Gyroelongated pentagonal cupolarotunda.png C5
48 Verlengde dubbelgedraaide vijfhoekige dubbelrotonde Johnson solid 48 net.png Gyroelongated pentagonal birotunda.png D5
49 Verhoogd driehoekig prisma Johnson solid 49 net.png Augmented triangular prism.png C2v
50 Dubbelverhoogd driehoekig prisma Johnson solid 50 net.png Biaugmented triangular prism.png C2v
51 Drievoudig verhoogd driehoekig prisma Johnson solid 51 net.png Triaugmented triangular prism.png D3h
52 Verhoogd vijfhoekig prisma Johnson solid 52 net.png Augmented pentagonal prism.png C2v
53 Dubbelverhoogd vijfhoekig prisma Johnson solid 53 net.png Biaugmented pentagonal prism.png C2v
54 Verhoogd zeshoekig prisma Johnson solid 54 net.png Augmented hexagonal prism.png C2v
55 Paradubbelverhoogd zeshoekig prisma Johnson solid 55 net.png Parabiaugmented hexagonal prism.png D2h
56 Metadubbelverhoogd zeshoekig prisma Johnson solid 56 net.png Metabiaugmented hexagonal prism.png C2v
57 Drievoudig verhoogd zeshoekig prisma Johnson solid 57 net.png Triaugmented hexagonal prism.png D3h
58 Verhoogde dodecaëder Johnson solid 58 net.png Augmented dodecahedron.png C5v
59 Paradubbelverhoogde dodecaëder Johnson solid 59 net.png Parabiaugmented dodecahedron.png D5d
60 Metadubbelverhoogde dodecaëder Johnson solid 60 net.png Metabiaugmented dodecahedron.png C2v
61 Drievoudig verhoogde dodecaëder Johnson solid 61 net.png Triaugmented dodecahedron.png C3v
62 Metadubbelverkleinde icosaëder Johnson solid 62 net.png Metabidiminished icosahedron.png C2v
63 Drievoudig verkleinde icosaëder Johnson solid 63 net.png Tridiminished icosahedron.png C3v
64 Verhoogde drievoudig verkleinde icosaëder Johnson solid 64 net.png Augmented tridiminished icosahedron.png C3v
65 Verhoogde afgeknotte tetraëder Johnson solid 65 net.png Augmented truncated tetrahedron.png C3v
66 Verhoogde afgeknotte kubus Johnson solid 66 net.png Augmented truncated cube.png C4v
67 Dubbelverhoogde afgeknotte kubus Johnson solid 67 net.png Biaugmented truncated cube.png D4h
68 Verhoogde afgeknotte dodecaëder Johnson solid 68 net.png Augmented truncated dodecahedron.png C5v
69 Paradubbelverhoogde afgeknotte dodecaëder Johnson solid 69 net.png Parabiaugmented truncated dodecahedron.png D5d
70 Metadubbelverhoogde afgeknotte dodecaëder Johnson solid 70 net.png Metabiaugmented truncated dodecahedron.png C2v
71 Drievoudig verhoogde afgeknotte dodecaëder Johnson solid 71 net.png Triaugmented truncated dodecahedron.png C3v
72 Gedraaide romboëdrisch icosidodecaëder Johnson solid 72 net.png Gyrate rhombicosidodecahedron.png C5v
73 Paradubbelgedraaide romboëdrisch icosidodecaëder Johnson solid 73 net.png Parabigyrate rhombicosidodecahedron.png D5d
74 Metadubbelgedraaide romboëdrisch icosidodecaëder Johnson solid 74 net.png Metabigyrate rhombicosidodecahedron.png C2v
75 Drievoudig gedraaide romboëdrisch icosidodecaëder Johnson solid 75 net.png Trigyrate rhombicosidodecahedron.png C3v
76 Verkleinde romboëdrisch icosidodecaëder Johnson solid 76 net.png Diminished rhombicosidodecahedron.png C5v
77 Paragedraaide verkleinde romboëdrisch icosidodecaëder Johnson solid 77 net.png Paragyrate diminished rhombicosidodecahedron.png C5v
78 Metagedraaide verkleinde romboëdrisch icosidodecaëder Johnson solid 78 net.png Metagyrate diminished rhombicosidodecahedron.png Cs
79 Dubbelgedraaide verkleinde romboëdrisch icosidodecaëder Johnson solid 79 net.png Bigyrate diminished rhombicosidodecahedron.png Cs
80 Paradubbelverkleinde romboëdrisch icosidodecaëder Johnson solid 80 net.png Parabidiminished rhombicosidodecahedron.png D5d
81 Metadubbelverkleinde romboëdrisch icosidodecaëder Johnson solid 81 net.png Metabidiminished rhombicosidodecahedron.png C2v
82 Gedraaide dubbelverkleinde romboëdrisch icosidodecaëder Johnson solid 82 net.png Gyrate bidiminished rhombicosidodecahedron.png Cs
83 Drievoudig verkleinde romboëdrisch icosidodecaëder Johnson solid 83 net.png Tridiminished rhombicosidodecahedron.png C3v
84 Siamese dodecaëder Johnson solid 84 net.png Snub disphenoid.png D2d
85 Siamees vierkant antiprisma Johnson solid 85 net.png Snub square antiprism.png D4d
86 Sphenocorona Johnson solid 86 net.png Sphenocorona.png C2v
87 Verhoogde sphenocorona Johnson solid 87 net.png Augmented sphenocorona.png Cs
88 Sphenomegacorona Johnson solid 88 net.png Sphenomegacorona.png C2v
89 Hebesphenomegacorona Johnson solid 89 net.png Hebesphenomegacorona.png C2v
90 Disphenocingulum Johnson solid 90 net.png Disphenocingulum.png D2d
91 Bilunabirotonde Johnson solid 91 net.png Bilunabirotunda.png D2h
92 Driehoekige hebesphenorotonde Johnson solid 92 net.png Triangular hebesphenorotunda.png C3v


Nummer Naam
(hoekpuntconfiguratie)
Afbeelding Openvouwing Vlakken Soort
vlakken
Ribben Knooppunten Symmetriegroep
1 Afgeknotte tetraëder
(3.6.6)
Truncated tetrahedron
(Animatie)
Truncated tetrahedron flat.svg 8 4 driehoeken
4 zeshoeken
18 12 Td
2 Kuboctaëder
(3.4.3.4)
Cuboctahedron
(Animatie)
Cuboctahedron flat.svg  14  8 driehoeken
6 vierkanten
24 12 Oh
3 Afgeknotte kubus
of afgeknotte hexaëder
(3.8.8)
Truncated hexahedron
(Animatie)
Truncated hexahedron flat.svg 14 8 driehoeken
6 achthoeken
36 24 Oh
4 Afgeknotte octaëder
(4.6.6)
Truncated octahedron

(Animatie)

Truncated octahedron flat.png 14 6 vierkanten
8 zeshoeken
36 24 Oh
5 Rombische kuboctaëder
of kleine rombische kuboctaëder
(3.4.4.4)
Rhombicuboctahedron
(Animatie)
Rhombicuboctahedron flat.png 26 8 driehoeken
18 vierkanten
48 24 Oh
6 Afgeknotte kuboctaëder
of grote rombische kuboctaëder
(4.6.8)
Truncated cuboctahedron
(Animatie)
Truncated cuboctahedron flat.svg 26 12 vierkanten
8 zeshoeken
6 achthoeken
72 48 Oh
7 Stompe kubus
of stompe hexaëder
(2 chirale vormen)
(3.3.3.3.4)
Snub hexahedron (Ccw)
(Animatie)
Snub hexahedron (Cw)
(Animatie)
Snub cube flat.svg 38 32 driehoeken
6 vierkanten
60 24 O
8 Icosidodecaëder
(3.5.3.5)
Icosidodecahedron
(Animatie)
Icosidodecahedron flat.svg 32 20 driehoeken
12 vijfhoeken
60 30 Ih
9 Afgeknotte dodecaëder
(3.10.10)
Truncated dodecahedron
(Animatie)
Truncated dodecahedron flat.png 32 20 driehoeken
12 tienhoeken
90 60 Ih
10 Afgeknotte icosaëder
(5.6.6)
Truncated icosahedron
(Animatie)
Truncated icosahedron flat-2.svg 32 12 vijfhoeken
20 zeshoeken
90 60 Ih
11 Rombische icosidodecaëder
of kleine rombische icosidodecaëder
(3.4.5.4)
Rhombicosidodecahedron
(Animatie)
Rhombicosidodecahedron flat.png 62 20 driehoeken
30 vierkanten
12 vijfhoeken
120 60 Ih
12 Afgeknotte icosidodecaëder
of grote rombische icosidodecaëder
(4.6.10)
Truncated icosidodecahedron
(Animatie)
Truncated icosidodecahedron flat.svg 62 30 vierkanten
20 zeshoeken
12 tienhoeken
180 120 Ih
13 Stompe dodecaëder
of afgeknotte icosidodecaëder
(2 chirale vormen)
(3.3.3.3.5)
Snub dodecahedron (Ccw)
(Animatie)
Snub dodecahedron (Cw)
(Animatie)
Snub dodecahedron flat.svg 92 80 driehoeken
12 vijfhoeken
150 60 I

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