|
01
Tetrahedron
Vertices: 4
Edges: 6
Faces: 4
Wythoff symbol: 3|2 3
Symmetry Group: {3, 3, 3}
Vertex Configuration: tetrahedral
Dual: tetrahedron
|
|
|
02
Truncated tetrahedron
Vertices: 12
Edges: 18
Faces: 8
Wythoff symbol: 2 3|3
Symmetry Group: tetrahedral
Vertex Configuration: {6, 6, 3}
Dual: triakis tetrahedron
|
|
|
03
Octahemioctahedron
Vertices: 12
Edges: 24
Faces: 12
Wythoff symbol: 3/2 3|3
Symmetry Group: tetrahedral
Vertex Configuration: {6, 3/2, 6, 3}
Dual: octahemioctacron
|
|
|
04
Tetrahemihexahedron
Vertices: 6
Edges: 12
Faces: 7
Wythoff symbol: 3/2 3|2
Symmetry Group: tetrahedral
Vertex Configuration: {4, 3/2, 4, 3}
Dual: tetrahemihexacron
|
|
|
05
Octahedron
Vertices: 6
Edges: 12
Faces: 8
Wythoff symbol: 4|2 3
Symmetry Group: octahedral
Vertex Configuration: {3, 3, 3, 3}
Dual: cube
|
|
|
06
Cube
Vertices: 8
Edges: 12
Faces: 6
Wythoff symbol: 3|2 4
Symmetry Group: octahedral
Vertex Configuration: {4, 4, 4}
Dual: octahedron
|
|
|
07
Cuboctahedron
Vertices: 12
Edges: 24
Faces: 14
Wythoff symbol: 2|3 4
Symmetry Group: octahedral
Vertex Configuration: {3, 4, 3, 4}
Dual: rhombic dodecahedron
|
|
|
08
Truncated octahedron
Vertices: 24
Edges: 36
Faces: 14
Wythoff symbol: 2 4|3
Symmetry Group: octahedral
Vertex Configuration: {6, 6, 4}
Dual: tetrakis hexahedron
|
|
|
09
Truncated cube
Vertices: 24
Edges: 36
Faces: 14
Wythoff symbol: 2 3|4
Symmetry Group: octahedral
Vertex Configuration: {8, 8, 3}
Dual: triakis octahedron
|
|
|
10
Rhombicuboctahedron
Vertices: 24
Edges: 48
Faces: 26
Wythoff symbol: 3 4|2
Symmetry Group: octahedral
Vertex Configuration: {4, 3, 4, 4}
Dual: deltoidal icositetrahedron
|
|
|
11
Truncated cuboctahedron
Vertices: 48
Edges: 72
Faces: 26
Wythoff symbol: 2 3 4|
Symmetry Group: octahedral
Vertex Configuration: {4, 6, 8}
Dual: disdyakis dodecahedron
|
|
|
12
Snub cube
Vertices: 24
Edges: 60
Faces: 38
Wythoff symbol: |2 3 4
Symmetry Group: octahedral
Vertex Configuration: {3, 3, 3, 3, 4}
Dual: pentagonal icositetrahedron
|
|
|
13
Small cubicuboctahedron
Vertices: 24
Edges: 48
Faces: 20
Wythoff symbol: 3/2 4|4
Symmetry Group: octahedral
Vertex Configuration: {8, 3/2, 8, 4}
Dual: small hexacronic icositetrahedron
|
|
|
14
Great cubicuboctahedron
Vertices: 24
Edges: 48
Faces: 20
Wythoff symbol: 3 4|4/3
Symmetry Group: octahedral
Vertex Configuration: {8/3, 3, 8/3, 4}
Dual: great hexacronic icositetrahedron
|
|
|
15
Cubohemioctahedron
Vertices: 12
Edges: 24
Faces: 10
Wythoff symbol: 4/3 4|3
Symmetry Group: octahedral
Vertex Configuration: {6, 4/3, 6, 4}
Dual: hexahemioctacron
|
|
|
16
Cubitruncated cuboctahedron
Vertices: 48
Edges: 72
Faces: 20
Wythoff symbol: 4/3 3 4|
Symmetry Group: octahedral
Vertex Configuration: {8/3, 6, 8}
Dual: tetradyakis hexahedron
|
|
|
17
Great rhombicuboctahedron
Vertices: 24
Edges: 48
Faces: 26
Wythoff symbol: 3/2 4|2
Symmetry Group: octahedral
Vertex Configuration: {4, 3/2, 4, 4}
Dual: great deltoidal icositetrahedron
|
|
|
18
Small rhombihexahedron
Vertices: 24
Edges: 48
Faces: 18
Wythoff symbol: 3/2 2 4|
Symmetry Group: octahedral
Vertex Configuration: {8, 4, 8/7, 4/3}
Dual: small rhombihexacron
|
|
|
19
Stellated truncated hexahedron
Vertices: 24
Edges: 36
Faces: 14
Wythoff symbol: 2 3|4/3
Symmetry Group: octahedral
Vertex Configuration: {8/3, 8/3, 3}
Dual: great triakis octahedron
|
|
|
20
Great truncated cuboctahedron
Vertices: 48
Edges: 72
Faces: 26
Wythoff symbol: 4/3 2 3|
Symmetry Group: octahedral
Vertex Configuration: {8/3, 4, 6}
Dual: great disdyakis dodecahedron
|
|
|
21
Great truncated cuboctahedron
Vertices: 24
Edges: 48
Faces: 18
Wythoff symbol: 4/3 3/2 2|
Symmetry Group: octahedral
Vertex Configuration: {4, 8/3, 4/3, 8/5}
Dual: great rhombihexacron
|
|
|
22
Icosahedron
Vertices: 12
Edges: 30
Faces: 20
Wythoff symbol: 5|2 3
Symmetry Group: icosahedral
Vertex Configuration: {3, 3, 3, 3, 3}
Dual: dodecahedron
|
|
|
23
Dodecahedron
Vertices: 20
Edges: 30
Faces: 12
Wythoff symbol: 3|2 5
Symmetry Group: icosahedral
Vertex Configuration: {5, 5, 5}
Dual: icosahedron
|
|
|
24
Icosidodecahedron
Vertices: 30
Edges: 60
Faces: 32
Wythoff symbol: 2|3 5
Symmetry Group: icosahedral
Vertex Configuration: {3, 5, 3, 5}
Dual: rhombic triacontahedron
|
|
|
25
Truncated icosahedron
Vertices: 60
Edges: 90
Faces: 32
Wythoff symbol: 2 5|3
Symmetry Group: icosahedral
Vertex Configuration: {6, 6, 5}
Dual: pentakis dodecahedron
|
|
|
26
Truncated dodecahedron
Vertices: 60
Edges: 90
Faces: 32
Wythoff symbol: 2 3|5
Symmetry Group: icosahedral
Vertex Configuration: {10, 10, 3}
Dual: triakis icosahedron
|
|
|
27
Rhombicosidodecahedron
Vertices: 60
Edges: 120
Faces: 62
Wythoff symbol: 3 5|2
Symmetry Group: icosahedral
Vertex Configuration: {4, 3, 4, 5}
Dual: deltoidal hexecontahedron
|
|
|
28
Truncated icosidodechedon
Vertices: 120
Edges: 180
Faces: 62
Wythoff symbol: 2 3 5|
Symmetry Group: icosahedral
Vertex Configuration: {4, 6, 10}
Dual: disdyakis triacontahedron
|
|
|
29
Snub dodecahedron
Vertices: 60
Edges: 150
Faces: 92
Wythoff symbol: |2 3 5
Symmetry Group: icosahedral
Vertex Configuration: {3, 3, 3, 3, 5}
Dual: pentagonal hexecontahedron
|
|
|
30
Small ditrigonal icosidodecahedron
Vertices: 20
Edges: 60
Faces: 32
Wythoff symbol: 3|5/2 3
Symmetry Group: icosahedral
Vertex Configuration: {5/2, 3, 5/2, 3, 5/2, 3}
Dual: small triambic icosahedron
|
|
|
31
Small icosicosidodecahedron
Vertices: 60
Edges: 120
Faces: 52
Wythoff symbol: 5/2 3|3
Symmetry Group: icosahedral
Vertex Configuration: {6, 5/2, 6, 3}
Dual: small icosacronic hexecontahedron
|
|
|
32
Small snub icosicosidodecahedron
Vertices: 60
Edges: 180
Faces: 112
Wythoff symbol: |5/2 3 3
Symmetry Group: icosahedral
Vertex Configuration: {3, 5/2, 3, 3, 3, 3}
Dual: small hexagonal hexecontahedron
|
|
|
33
Small dodecicosidodecahedron
Vertices: 60
Edges: 120
Faces: 44
Wythoff symbol: 3/2 5|5
Symmetry Group: icosahedral
Vertex Configuration: {10, 3/2, 10, 5}
Dual: small dodecacronic hexecontahedron
|
|
|
34
Small stellated dodecahedron
Vertices: 12
Edges: 30
Faces: 12
Wythoff symbol: 5|2 5/2
Symmetry Group: icosahedral
Vertex Configuration: {5/2, 5/2, 5/2, 5/2, 5/2}
Dual: great dodecahedron
|
|
|
35
Great dodecahedron
Vertices: 12
Edges: 30
Faces: 12
Wythoff symbol: 5/2|2 5
Symmetry Group: icosahedral
Vertex Configuration: {5, 5, 5, 5, 5}/2
Dual: small stellated dodecahedron
|
|
|
36
Dodecadodecahedron
Vertices: 30
Edges: 60
Faces: 24
Wythoff symbol: 2|5/2 5
Symmetry Group: icosahedral
Vertex Configuration: {5/2, 5, 5/2, 5}
Dual: medial rhombic triacontahedron
|
|
|
37
Truncated great dodecahedron
Vertices: 60
Edges: 90
Faces: 24
Wythoff symbol: 2 5/2|5
Symmetry Group: icosahedral
Vertex Configuration: {10, 10, 5/2}
Dual: small stellapentakis dodecahedron
|
|
|
38
Rhombidodecadodecahedron
Vertices: 60
Edges: 120
Faces: 54
Wythoff symbol: 5/2 5|2
Symmetry Group: icosahedral
Vertex Configuration: {4, 5/2, 4, 5}
Dual: medial deltoidal hexecontahedron
|
|
|
39
Small rhombidodecahedron
Vertices: 60
Edges: 120
Faces: 42
Wythoff symbol: 2 5/2 5|
Symmetry Group: icosahedral
Vertex Configuration: {10, 4, 10/9, 4/3}
Dual: small rhombidodecacron
|
|
|
40
Snub dodecadodecahedron
Vertices: 60
Edges: 150
Faces: 84
Wythoff symbol: |2 5/2 5
Symmetry Group: icosahedral
Vertex Configuration: {3, 3, 5/2, 3, 5}
Dual: medial pentagonal hexecontahedron
|
|
|
41
Ditrigonal dodecadodecahedron
Vertices: 20
Edges: 60
Faces: 24
Wythoff symbol: 3|5/3 5
Symmetry Group: icosahedral
Vertex Configuration: {5/3, 5, 5/3, 5, 5/3, 5}
Dual: medial triambic icosahedron
|
|
|
42
Great ditrigonal dodecicosidodecahedron
Vertices: 60
Edges: 120
Faces: 44
Wythoff symbol: 3 5|5/3
Symmetry Group: icosahedral
Vertex Configuration: {10/3, 3, 10/3, 5}
Dual: great ditrigonal dodecacronic hexecontahedron
|
|
|
43
Small ditrigonal dodecicosidodecahedron
Vertices: 60
Edges: 120
Faces: 44
Wythoff symbol: 5/3 3|5
Symmetry Group: icosahedral
Vertex Configuration: {10, 5/3, 10, 3}
Dual: small ditrigonal dodecacronic hexecontahedron
|
|
|
44
Icosidodecadodecahedron
Vertices: 60
Edges: 120
Faces: 44
Wythoff symbol: 5/3 5|3
Symmetry Group: icosahedral
Vertex Configuration: {6, 5/3, 6, 5}
Dual: medial icosacronic hexecontahedron
|
|
|
45
Icositruncated dodecadodecahedron
Vertices: 120
Edges: 180
Faces: 44
Wythoff symbol: 5/3 3 5|
Symmetry Group: icosahedral
Vertex Configuration: {10/3, 6, 10}
Dual: tridyakis icosahedron
|
|
|
46
Snub icosidodecadodecahedron
Vertices: 60
Edges: 180
Faces: 104
Wythoff symbol: |5/3 3 5
Symmetry Group: icosahedral
Vertex Configuration: {3, 5/3, 3, 3, 3, 5}
Dual: medial hexagonal hexecontahedron
|
|
|
47
Great ditrigonal icosidodecahedron
Vertices: 20
Edges: 60
Faces: 32
Wythoff symbol: 3/2|3 5
Symmetry Group: icosahedral
Vertex Configuration: {3, 5, 3, 5, 3, 5}/2
Dual: great triambic icosahedron
|
|
|
48
Great icosicosidodecahedron
Vertices: 60
Edges: 120
Faces: 52
Wythoff symbol: 3/2 5|3
Symmetry Group: icosahedral
Vertex Configuration: {6, 3/2, 6, 5}
Dual: great icosacronic hexecontahedron
|
|
|
49
Small icosihemidodecahedron
Vertices: 30
Edges: 60
Faces: 26
Wythoff symbol: 3/2 3|5
Symmetry Group: icosahedral
Vertex Configuration: {10, 3/2, 10, 3}
Dual: small icosihemidodecacron
|
|
|
50
Small dodecicosahedron
Vertices: 60
Edges: 120
Faces: 32
Wythoff symbol: 3/2 3 5|
Symmetry Group: icosahedral
Vertex Configuration: {10, 6, 10/9, 6/5}
Dual: small dodecicosacron
|
|
|
51
Small dodecahemidodecahedron
Vertices: 30
Edges: 60
Faces: 18
Wythoff symbol: 5/4 5|5
Symmetry Group: icosahedral
Vertex Configuration: {10, 5/4, 10, 5}
Dual: small dodecahemidodecacron
|
|
|
52
Great stellated dodecahedron
Vertices: 20
Edges: 30
Faces: 12
Wythoff symbol: 3|2 5/2
Symmetry Group: icosahedral
Vertex Configuration: {5/2, 5/2, 5/2}
Dual: great icosahedron
|
|
|
53
Great icosahedron
Vertices: 12
Edges: 30
Faces: 20
Wythoff symbol: 5/2|2 3
Symmetry Group: icosahedral
Vertex Configuration: {3, 3, 3, 3, 3}/2
Dual: great stellated dodecahedron
|
|
|
54
Great icosidodecahedron
Vertices: 30
Edges: 60
Faces: 32
Wythoff symbol: 2|5/2 3
Symmetry Group: icosahedral
Vertex Configuration: {5/2, 3, 5/2, 3}
Dual: great rhombic triacontahedron
|
|
|
55
Great truncated icosahedron
Vertices: 60
Edges: 90
Faces: 32
Wythoff symbol: 2 5/2|3
Symmetry Group: icosahedral
Vertex Configuration: {6, 6, 5/2}
Dual: great stellapentakis dodecahedron
|
|
|
56
Rhombicosahedron
Vertices: 60
Edges: 120
Faces: 50
Wythoff symbol: 2 5/2 3|
Symmetry Group: icosahedral
Vertex Configuration: {6, 4, 6/5, 4/3}
Dual: rhombicosacron
|
|
|
57
Great snub icosidodecahedron
Vertices: 60
Edges: 150
Faces: 92
Wythoff symbol: |2 5/2 3
Symmetry Group: icosahedral
Vertex Configuration: {3, 3, 5/2, 3, 3}
Dual: great pentagonal hexecontahedron
|
|
|
58
Small stellated truncated dodecahedron
Vertices: 60
Edges: 90
Faces: 24
Wythoff symbol: 2 5|5/3
Symmetry Group: icosahedral
Vertex Configuration: {10/3, 10/3, 5}
Dual: great pentakis dodecahedron
|
|
|
59
Truncated dodecadodecahedron
Vertices: 120
Edges: 180
Faces: 54
Wythoff symbol: 5/3 2 5|
Symmetry Group: icosahedral
Vertex Configuration: {10/3, 4, 10}
Dual: medial disdyakis triacontahedron
|
|
|
60
Inverted snub dodecadodecahedron
Vertices: 60
Edges: 150
Faces: 84
Wythoff symbol: |5/3 2 5
Symmetry Group: icosahedral
Vertex Configuration: {3, 5/3, 3, 3, 5}
Dual: medial inverted pentagonal hexecontahedron
|
|
|
61
Great dodecicosidodecahedron
Vertices: 60
Edges: 120
Faces: 44
Wythoff symbol: 5/2 3|5/3
Symmetry Group: icosahedral
Vertex Configuration: {10/3, 5/2, 10/3, 3}
Dual: great dodecacronic hexecontahedron
|
|
|
62
Small dodecahemicosahedron
Vertices: 30
Edges: 60
Faces: 22
Wythoff symbol: 5/3 5/2|3
Symmetry Group: icosahedral
Vertex Configuration: {6, 5/3, 6, 5/2}
Dual: small dodecahemicosacron
|
|
|
63
Great dodecicosahedron
Vertices: 60
Edges: 120
Faces: 32
Wythoff symbol: 5/3 5/2 3|
Symmetry Group: icosahedral
Vertex Configuration: {6, 10/3, 6/5, 10/7}
Dual: great dodecicosacron
|
|
|
64
Great snub dodecicosidodecahedron
Vertices: 60
Edges: 180
Faces: 104
Wythoff symbol: |5/3 5/2 3
Symmetry Group: icosahedral
Vertex Configuration: {3, 5/3, 3, 5/2, 3, 3}
Dual: great hexagonal hexecontahedron
|
|
|
65
Great dodecahemicosahedron
Vertices: 30
Edges: 60
Faces: 22
Wythoff symbol: 5/4 5|3
Symmetry Group: icosahedral
Vertex Configuration: {6, 5/4, 6, 5}
Dual: great dodecahemicosacron
|
|
|
66
Great stellated truncated dodecahedron
Vertices: 60
Edges: 90
Faces: 32
Wythoff symbol: 2 3|5/3
Symmetry Group: icosahedral
Vertex Configuration: {10/3, 10/3, 3}
Dual: great triakis icosahedron
|
|
|
67
Great rhombicosidodecahedron
Vertices: 60
Edges: 120
Faces: 62
Wythoff symbol: 5/3 3|2
Symmetry Group: icosahedral
Vertex Configuration: {4, 5/3, 4, 3}
Dual: great deltoidal hexecontahedron
|
|
|
68
Great truncated icosidodecahedron
Vertices: 120
Edges: 180
Faces: 62
Wythoff symbol: 5/3 2 3|
Symmetry Group: icosahedral
Vertex Configuration: {10/3, 4, 6}
Dual: great disdyakis triacontahedron
|
|
|
69
Great inverted snub icosidodecahedron
Vertices: 60
Edges: 150
Faces: 92
Wythoff symbol: |5/3 2 3
Symmetry Group: icosahedral
Vertex Configuration: {3, 5/3, 3, 3, 3}
Dual: great inverted pentagonal hexecontahedron
|
|
|
70
Great dodecahemidodecahedron
Vertices: 30
Edges: 60
Faces: 18
Wythoff symbol: 5/3 5/2|5/3
Symmetry Group: icosahedral
Vertex Configuration: {10/3, 5/3, 10/3, 5/2}
Dual: great dodecahemidodecacron
|
|
|
71
Great icosihemidodecahedron
Vertices: 30
Edges: 60
Faces: 26
Wythoff symbol: 3/2 3|5/3
Symmetry Group: icosahedral
Vertex Configuration: {10/3, 3/2, 10/3, 3}
Dual: great icosihemidodecacron
|
|
|
72
Small retrosnub icosicosidodecahedron
Vertices: 60
Edges: 180
Faces: 112
Wythoff symbol: |3/2 3/2 5/2
Symmetry Group: icosahedral
Vertex Configuration: {3, 3/2, 3, 3/2, 3, 5/2}
Dual: small hexagrammic hexecontahedron
|
|
|
73
Great rhombidodecahedron
Vertices: 60
Edges: 120
Faces: 42
Wythoff symbol: 3/2 5/3 2|
Symmetry Group: icosahedral
Vertex Configuration: {4, 10/3, 4/3, 10/7}
Dual: great rhombidodecacron
|
|
|
74
Great retrosnub icosidodecahedron
Vertices: 60
Edges: 150
Faces: 92
Wythoff symbol: |3/2 5/3 2
Symmetry Group: icosahedral
Vertex Configuration: {3, 3/2, 3, 5/3, 3}
Dual: great pentagrammic hexecontahedron
|
|
|
75
Great dirhombicosidodecahedron
Vertices: 60
Edges: 240
Faces: 124
Wythoff symbol: |3/2 5/3 3 5/2
Symmetry Group: icosahedral
Vertex Configuration: {4, 5/3, 4, 3, 4, 5/2, 4, 3/2}
Dual: great dirhombicosidodecacron
|
|
|
76
Pentagonal prism
Vertices: 10
Edges: 15
Faces: 7
Wythoff symbol: 2 5|2
Symmetry Group: dihedral
Vertex Configuration: {4, 4, 5}
Dual: pentagonal dipyramid
|
|
|
77
Pentagonal antiprism
Vertices: 10
Edges: 20
Faces: 12
Wythoff symbol: |2 2 5
Symmetry Group: dihedral
Vertex Configuration: {3, 3, 3, 5}
Dual: pentagonal trapezohedron
|
|
|
78
Pentagrammic prism
Vertices: 10
Edges: 15
Faces: 7
Wythoff symbol: 2 5/2|2
Symmetry Group: dihedral
Vertex Configuration: {4, 4, 5/2}
Dual: pentagrammic dipyramid
|
|
|
79
Pentagrammic antiprism
Vertices: 10
Edges: 20
Faces: 12
Wythoff symbol: |2 2 5/2
Symmetry Group: dihedral
Vertex Configuration: {3, 3, 3, 5/2}
Dual: pentagrammic deltahedron
|
|
|
80
Pentagrammic crossed antiprism
Vertices: 10
Edges: 20
Faces: 12
Wythoff symbol: |2 2 5/3
Symmetry Group: dihedral
Vertex Configuration: {3, 3, 3, 5/3}
Dual: pentagrammic concave deltahedron
|
|
