Truncated dodecahedron
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Truncated dodecahedron | |
---|---|
Truncated dodecahedron Click on picture for large version. Click here for spinning version. | |
Type | Archimedean |
Faces | 20 triangles 12 decagons |
Edges | 90 |
Vertices | 60 |
Vertex configuration | 3,10,10 |
Symmetry group | icosahedral (I_{h}) |
Dual polyhedron | triakis icosahedron |
Properties | convex, semi-regular (vertex-uniform) |
The truncated dodecahedron is an Archimedean solid. It has 12 regular decagonal faces, 20 regular triangular faces, 60 vertices and 90 edges.
Canonical coordinates
Canonical coordinates for the vertices of a truncated dodecahedron centered at the origin are (0, ±1/τ, ±(2+τ)), (±(2+τ), 0, ±1/τ), (±1/τ, ±(2+τ), 0), and (±1/τ, ±τ, ±2τ), (±2τ, ±1/τ, ±τ), (±τ, ±2τ, ±1/τ), and (±τ, ±2, ±τ^{2}), (±τ^{2}, ±τ, ±2), (±2, ±τ^{2}, ±τ), where τ = (1+√5)/2 is the golden mean.
Geometric relations
This polyhedra can be formed by taking a dodecahedron and truncating (cutting) off the corners so the pentagon faces become decagons and the corners become triangles.
See also
External links
- The Uniform Polyhedra
- Virtual Reality Polyhedra The Encyclopedia of Polyhedra