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.

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