Pentakis dodecahedron
From Wikipedia, the free encyclopedia
| Pentakis dodecahedron | |
|---|---|
 (Click here for rotating model) |
|
| Type | Catalan solid |
| Face type | isosceles triangle |
| Faces | 60 |
| Edges | 90 |
| Vertices | 32 |
| Vertices by type | 20{3}+12{10} |
| Face configuration | V5.6.6 |
| Symmetry group | Ih |
| Dihedral angle | 156°43'7" |
| Dual | Truncated icosahedron |
| Properties | convex, face-transitive |
A pentakis dodecahedron is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated icosahedron.
It can be seen as a dodecahedron with a pentagonal pyramid covering each face. This interpretion is expressed in its name.
Contents |
[edit] Chemistry
The pentakis dodecahedron in a model of buckminsterfullerene: each surface segment represents a carbon atom]].
[edit] Cultural references
- Spaceship Earth in Walt Disney World's Epcot is based on one.
- The shape of the 'Crystal Dome' used in the popular TV game show The Crystal Maze is based on a pentakis dodecahedron.
[edit] References
- Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. (Section 3-9)
[edit] External links
- Eric W. Weisstein, Pentakis dodecahedron at MathWorld.
