Solids with 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 meetingat 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 triangles12 pentagons | 60 | 30 | 3,5,3,5 |
| truncated dodecahedron | (Video) | 32 | 20 triangles12 decagons | 90 | 60 | 3,10,10 |
| truncated icosahedronor commonly football (soccer ball) | (Video) | 32 | 12 pentagons20 hexagons | 90 | 60 | 5,6,6 |
| rhombicosidodecahedronor small rhombicosidodecahedron | (Video) | 62 | 20 triangles30 squares12 pentagons | 120 | 60 | 3,4,5,4 |
| truncated icosidodecahedronor great rhombicosidodecahedron | (Video) | 62 | 30 squares20 hexagons12 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 triacontahedronor hexakis icosahedron | (Video) | truncated icosidodecahedron | 120 | 180 | 62 | scalene triangle |
Kepler-Poinsot solids
Achiral nonconvex uniform polyhedra
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Chiral Archimedean and Catalan solids
| Name | picture | Faces | Edges | Vertices | Vertex configuration | |
|---|---|---|---|---|---|---|
| snub dodecahedronor snub icosidodecahedron (2 chiral forms) |  (Video) (Video) | 92 | 80 triangles12 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
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Construction
Construction instructions for the following solids are available: Platonic solids,[1]Archimedean solids,[2]Achiral Catalan solids,[3]Kepler–Poinsot solids,[4]Achiral nonconvex uniform polyhedra,[5] Chiral Archimedean and Catalan solids: Snub dodecahedron[6] and Pentagonal hexecontahedron,[7] and Chiral nonconvex uniform polyhedra.[8]
See also
Citations
- ↑Wenninger 1971, pp. 17–19.
- ↑Wenninger 1971, pp. 23–24, 26, 28, 30.
- ↑Wenninger 1983, pp. 14–35.
- ↑Wenninger 1971, pp. 38–40, 63.
- ↑Wenninger 1971, pp. 106–117, 123–131, 135–143, 147–158, 161–170, 200–203.
- ↑Wenninger 1971, p. 32.
- ↑Wenninger 1983, p. 29.
- ↑Wenninger 1971, pp. 172–199.
Works cited
Category:
- Rotational symmetry