Trapezo-rhombic dodecahedron
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| Trapezo-rhombic dodecahedron | |
|---|---|
 |
|
| Type | Johnson solid dual |
| Faces | 6 rhombus, 6 trapezoid |
| Edges | 24 |
| Vertices | 14 |
| Vertex configuration | (2) 4.4.4 (6) 4.4.4.4 (6) 4.4.4 |
| Symmetry group | Dihedral (D3h) |
| Dual polyhedron | Triangular orthobicupola |
| Properties | convex, zonohedron |
The Trapezo-rhombic dodecahedron is a convex polyhedron with 6 rhombic and 6 trapezoidal faces.
This shape could be constructed by taking a tall uniform hexagonal prism, and making 3 angled cuts on the top and bottom. The trapezoids represent what remains of the original prism sides, and the 6 rhombi a result of the top and bottom cuts.
A space-filling tessellation (or honeycomb) can be made by translated copies of this cell. Each "layer" is a hexagonal tiling, and alternate layers are connected by shifting their centers so the rhombic faces match up.
It is the polyhedral dual of the triangular orthobicupola.
[edit] External links
[edit] References
- Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X.
