# Solids with icosahedral symmetry

Main article: Icosahedral symmetry

## Solids with full icosahedral symmetry

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

 {5,3} {3,5}

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

Catalan solids - duals of the Archimedean solids.

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

### Platonic solids

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

(Animation)

12 30 20 5 3
icosahedron

(Animation)

20 30 12 3 5

### Achiral Archimedean solids

Name picture Faces Edges Vertices Vertex configuration
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

Name picture Dual Archimedean solid Faces Edges Vertices Face Polygon
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

## Chiral Archimedean and Catalan solids

Name picture Faces Edges Vertices Vertex configuration
snub dodecahedron
or snub icosidodecahedron (2 chiral forms)

(Video)

(Video)
92 80 triangles
12 pentagons
150 60 3,3,3,3,5
Name picture Dual Archimedean solid Faces Edges Vertices Face Polygon
pentagonal hexecontahedron
(Video)(Video)
snub dodecahedron 60 50 92 irregular pentagon