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Pentagonal bifrustum
Convex polyhedron
Convex polyhedron
| Field | Value |
|---|---|
| name | Pentagonal Bifrustum |
| image | Dual elongated pentagonal dipyramid.png |
| caption | |
| type | Bifrustum |
| euler | |
| faces | 10 trapezoids |
| 2 pentagons | |
| edges | 25 |
| vertices | 15 |
| vertex_config | |
| schläfli | |
| wythoff | |
| conway | |
| coxeter | |
| symmetry | *D*5h |
| rotation_group | |
| surface_area | |
| volume | |
| angle | |
| dual | Elongated pentagonal dipyramid |
| properties | Convex |
| vertex_figure | |
| net | Dual elongated pentagonal dipyramid net.png |
| net_caption |
2 pentagons
In geometry, the pentagonal bifrustum or truncated pentagonal bipyramid is the third in an infinite series of bifrustum polyhedra. It has 10 trapezoidal and 2 pentagonal faces.
Constructions
The pentagonal bifrustum is the dual polyhedron of a Johnson solid, the elongated pentagonal bipyramid.
This polyhedron can be constructed by taking a pentagonal bipyramid and truncating the polar axis vertices. In Conway polyhedron notation, it can be represented as the polyhedron "t5dP5", meaning the truncation of the degree-five vertices of the dual of a pentagonal prism.
Alternatively, it can be constructed by gluing together two end-to-end pentagonal frustums, or (if coplanar faces are allowed) by gluing together two pentagonal prisms on their pentagonal faces.
Application
In nanoparticles, a 15-site truncated pentagonal bipyramid structure may form the nucleus of larger twinned structures with five-fold or icosahedral symmetry.
References
References
- [http://www.georgehart.com/virtual-polyhedra/conway_notation.html Conway Notation for Polyhedra], [[George W. Hart]], accessed 2014-12-20.
- Hofmeister, Herbert. (1999). "Fivefold twinning in nanosized particles and nanocrystalline thin films – ubiquitous metastable structures". Materials Science Forum.
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