triangular bifrustum
{{short description|Polyhedron created by truncating a triangular bipyramid}}
{{Infobox polyhedron
| name = Triangular bifrustum
| image = Dual elongated triangular dipyramid.png
| caption =
| type = Bifrustum
| euler =
| faces = 6 trapezoids,
2 triangles
| edges = 15
| vertices = 9
| vertex_config =
| schläfli =
| wythoff =
| coxeter =
| symmetry = {{math|Symmetry group#Three dimensions}}
| surface_area =
| volume =
| angle =
| dual = Elongated triangular bipyramid
| properties = convex
| vertex_figure =
| net = Dual_elongated_triangular_dipyramid_net.png
}}
In geometry, the triangular bifrustum is the second in an infinite series of bifrustum polyhedra. It has 6 trapezoid and 2 triangle faces. It may also be called the truncated triangular bipyramid; however, that term is ambiguous, as it may also refer to polyhedra formed by truncating all five vertices of a triangular bipyramid.For instance, Haji-Akbari et al. use it in the latter sense: see {{citation
| last1 = Haji-Akbari | first1 = Amir
| last2 = Chen | first2 = Elizabeth R.
| last3 = Engel | first3 = Michael
| last4 = Glotzer | first4 = Sharon C.
| arxiv = 1304.3147
| journal = Phys. Rev. E
| page = 012127
| title = Packing and self-assembly of truncated triangular bipyramids
| volume = 88
| year = 2013 | issue = 1
| doi=10.1103/physreve.88.012127| pmid = 23944434
| bibcode = 2013PhRvE..88a2127H| s2cid = 8184675
}}.
This polyhedron can be constructed by taking a triangular bipyramid and truncating the polar axis vertices, making it into two end-to-end frustums. It appears as the form of certain nanocrystals.{{citation
| last1 = Kharisov | first1 = Boris I.
| last2 = Kharissova | first2 = Oxana Vasilievna | author2-link = Oxana Kharissova
| last3 = Ortiz-Mendez | first3 = Ubaldo
| isbn = 9781439853436
| page = 466
| publisher = CRC Press
| title = Handbook of Less-Common Nanostructures
| url = https://books.google.com/books?id=yhRNwE7oMPYC&pg=PA466
| year = 2012}}.{{citation
| last1 = Yoo | first1 = Hyojong
| last2 = Millstone | first2 = Jill E.
| last3 = Li | first3 = Shuzhou
| last4 = Jang | first4 = Jae-Won
| last5 = Wei | first5 = Wei
| last6 = Wu | first6 = Jinsong
| last7 = Schatz | first7 = George C.
| last8 = Mirkin | first8 = Chad A.
| doi = 10.1021/nl901513g
| issue = 8
| journal = Nano Letters
| pages = 3038–3041
| pmid = 19603815
| title = Core–Shell Triangular Bifrustums
| volume = 9
| year = 2009 | pmc=3930336| bibcode = 2009NanoL...9.3038Y}}.
A truncated triangular bipyramid can be constructed by connecting two stacked regular octahedra with 3 pairs of tetrahedra around the sides. This represents a portion of the gyrated alternated cubic honeycomb.
References
{{reflist}}
External links
- [http://www.georgehart.com/virtual-polyhedra/conway_notation.html Conway Notation for Polyhedra] Try: t3dP3