Related Polyhedra
It shares the same edge arrangement as the convex regular icosahedron.
If the great dodecahedron is considered as a properly intersected surface geometry, it has the same topology as a triakis icosahedron with concave pyramids rather than convex ones.
A truncation process applied to the great dodecahedron produces a series of nonconvex uniform polyhedra. Truncating edges down to points produces the dodecadodecahedron as a rectified great dodecahedron. The process completes as a birectification, reducing the original faces down to points, and producing the small stellated dodecahedron.
The truncated small stellated dodecahedron looks like a dodecahedron on the surface, but it has 24 pentagonal faces: 12 as the truncation facets of the former vertices, and 12 more (coinciding with the first set) as truncated pentagrams.
| Name | Small stellated dodecahedron | Truncated small stellated dodecahedron | Dodecadodecahedron | Truncated great dodecahedron |
Great dodecahedron |
|---|---|---|---|---|---|
| Coxeter-Dynkin diagram |
|||||
| Picture |
Read more about this topic: Great Dodecahedron
Famous quotes containing the word related:
“A parent who from his own childhood experience is convinced of the value of fairy tales will have no difficulty in answering his child’s questions; but an adult who thinks these tales are only a bunch of lies had better not try telling them; he won’t be able to related them in a way which would enrich the child’s life.”
—Bruno Bettelheim (20th century)