Solids with icosahedral symmetry

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Main article: Icosahedral symmetry

## Solids with full icosahedral symmetry

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Platonic solids \- regular polyhedra (all faces of the same type)

{5,3}  |
{3,5}

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Archimedean solids \- polyhedra with more than one polygon face type.

3.10.10  |
4.6.10  |
5.6.6  |
3.4.5.4  |
3.5.3.5

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Catalan solids \- duals of the Archimedean solids.

V3.10.10  |
V4.6.10  |
V5.6.6  |
V3.4.5.4  |
V3.5.3.5

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### Platonic solids

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Name  | Picture  | Faces  | Edges  | Vertices  | Edges per face  | Faces meeting
at each vertex

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dodecahedron |

(Animation)

| 12 | 30 | 20 | 5 | 3
icosahedron |

(Animation)

| 20 | 30 | 12 | 3 | 5

### Achiral Archimedean solids

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Name  | picture  | Faces  | Edges  | Vertices  | Vertex configuration

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icosidodecahedron
(quasi-regular: vertex- and edge-uniform)  |
(Video) | 32 | 20 triangles
12 pentagons | 60 | 30  | 3,5,3,5
truncated dodecahedron |
(Video) | 32 | 20 triangles
12 decagons | 90  | 60  | 3,10,10
truncated icosahedron
or commonly football (soccer ball)  |
(Video) | 32 | 12 pentagons
20 hexagons | 90  | 60  | 5,6,6
rhombicosidodecahedron
or small rhombicosidodecahedron  |
(Video) | 62 | 20 triangles
30 squares
12 pentagons  | 120 | 60 | 3,4,5,4
truncated icosidodecahedron
or great rhombicosidodecahedron  |
(Video) | 62 | 30 squares
20 hexagons
12 decagons  | 180 | 120 | 4,6,10

### Achiral Catalan solids

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Name  | picture  | Dual Archimedean solid  | Faces  | Edges  | Vertices  | Face Polygon

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rhombic triacontahedron
(quasi-regular dual: face- and edge-uniform)  |
(Video) | icosidodecahedron | 30  | 60  | 32  | rhombus
triakis icosahedron |
(Video) | truncated dodecahedron | 60  | 90  | 32  | isosceles triangle
pentakis dodecahedron |
(Video) | truncated icosahedron | 60  | 90  | 32  | isosceles triangle
deltoidal hexecontahedron |
(Video) | rhombicosidodecahedron | 60  | 120  | 62  | kite
disdyakis triacontahedron
or hexakis icosahedron  |
(Video) | truncated icosidodecahedron | 120  | 180  | 62  | scalene triangle

### Kepler-Poinsot solids

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### Achiral nonconvex uniform polyhedra

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## Chiral Archimedean and Catalan solids

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Archimedean solids:

Name  | picture  | Faces  | Edges  | Vertices  | Vertex configuration

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snub dodecahedron
or snub icosidodecahedron (2 chiral forms)  |
(Video)

(Video) | 92 | 80 triangles
12 pentagons | 150  | 60  | 3,3,3,3,5

Catalan solids:

Name  | picture  | Dual Archimedean solid  | Faces  | Edges  | Vertices  | Face Polygon

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pentagonal hexecontahedron |
(Video)(Video) | snub dodecahedron | 60  | 50  | 92  | irregular pentagon

## Chiral nonconvex uniform polyhedra

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## See also

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* The Fifty Nine Icosahedra