| 释义 |
- Solids with full icosahedral symmetry Platonic solids Achiral Archimedean solids Achiral Catalan solids Kepler-Poinsot solids
- Chiral Archimedean and Catalan solids
- Chiral nonconvex uniform polyhedra
- See also
{{main|Icosahedral symmetry}}Solids with full icosahedral symmetryPlatonic solids - regular polyhedra (all faces of the same type) 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 | |
Kepler-Poinsot solids===Achiral nonconvex uniform polyhedra=== Chiral Archimedean and Catalan solidsArchimedean 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 |
Catalan solids: | 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 See also - The Fifty Nine Icosahedra
1 : Rotational symmetry |