Solids with icosahedral symmetry
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Solids with full icosahedral symmetry[edit]
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[edit]
| Name | Picture | Faces | Edges | Vertices | Edges per face | Faces meeting at each vertex |
|---|---|---|---|---|---|---|
| dodecahedron | |
12 | 30 | 20 | 5 | 3 |
| icosahedron | |
20 | 30 | 12 | 3 | 5 |
Achiral Archimedean solids[edit]
| 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[edit]
| 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 |
Kepler-Poinsot solids[edit]
Achiral nonconvex uniform polyhedra[edit]
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Chiral Archimedean and Catalan solids[edit]
| 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 |
Chiral nonconvex uniform polyhedra[edit]
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