Triangular bifrustum
Polyhedron created by truncating a triangular bipyramid
title: "Triangular bifrustum" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["polyhedra"] description: "Polyhedron created by truncating a triangular bipyramid" topic_path: "general/polyhedra" source: "https://en.wikipedia.org/wiki/Triangular_bifrustum" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::summary Polyhedron created by truncating a triangular bipyramid ::
::data[format=table title="Infobox polyhedron"]
| Field | Value |
|---|---|
| name | Triangular bifrustum |
| image | Dual elongated triangular dipyramid.png |
| type | Bifrustum |
| faces | 6 trapezoids, |
| 2 triangles | |
| edges | 15 |
| vertices | 9 |
| symmetry | D |
| dual | Elongated triangular bipyramid |
| properties | convex |
| net | Dual_elongated_triangular_dipyramid_net.png |
| :: |
| 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 = D | 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 | article-number = 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 = 978-1-4398-5343-6 | 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. :[[File:Triangulated truncated triangular bipyramid.png|240px]]
References
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