Biaugmented triangular prism: Difference between revisions
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In [[geometry]], the '''biaugmented triangular prism''' is a polyhedron constructed from a [[triangular prism]] by attaching two [[equilateral square pyramid]]s onto two of its square [[face (geometry)|faces]]. It is an example of [[Johnson solid]]. |
In [[geometry]], the '''biaugmented triangular prism''' is a polyhedron constructed from a [[triangular prism]] by attaching two [[equilateral square pyramid]]s onto two of its square [[face (geometry)|faces]]. It is an example of [[Johnson solid]]. |
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== Construction == |
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The biaugmented triangular prism can be constructed from a [[triangular prism]] by attaching two [[equilateral square pyramid]]s onto its two square faces, a process known as [[Augmentation (geometry)|augmentation]].{{r|rajwade}} These square pyramid covers the square face of the prism, so the resulting polyhedron has 10 [[equilateral triangle]]s and 1 [[Square (geometry)|square]] as its faces.{{r|berman}} A [[Convex set|convex]] polyhedron in which all faces are [[Regular polygon|regular]] is [[Johnson solid]], and the biaugmented triangular prism is among them, enumerated as 50th Johnson solid <math> J_{50} </math>.{{r|francis}} |
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== See also == |
== See also == |
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* [[Augmented triangular prism]] — the 39th Johnson solid, constructed by attaching a triangular prism with one equilateral square pyramid. |
* [[Augmented triangular prism]] — the 39th Johnson solid, constructed by attaching a triangular prism with one equilateral square pyramid. |
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* [[Triaugmented triangular prism]] — the 51st Johnson solid, constructed by attaching a triangular prism with three equilateral square pyramids. |
* [[Triaugmented triangular prism]] — the 51st Johnson solid, constructed by attaching a triangular prism with three equilateral square pyramids. |
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== References == |
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{{reflist|refs= |
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<ref name="berman">{{cite journal |
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| last = Berman | first = Martin |
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| year = 1971 |
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| title = Regular-faced convex polyhedra |
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| journal = Journal of the Franklin Institute |
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| volume = 291 |
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| issue = 5 |
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| pages = 329–352 |
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| doi = 10.1016/0016-0032(71)90071-8 |
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| mr = 290245 |
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}}</ref> |
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<ref name="francis">{{cite journal |
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| last = Francis | first = Darryl |
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| title = Johnson solids & their acronyms |
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| journal = Word Ways |
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| date = August 2013 |
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| volume = 46 | issue = 3 | page = 177 |
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| url = https://go.gale.com/ps/i.do?id=GALE%7CA340298118 |
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}}</ref> |
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<ref name="rajwade">{{cite book |
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| last = Rajwade | first = A. R. |
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| title = Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem |
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| series = Texts and Readings in Mathematics |
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| year = 2001 |
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| url = https://books.google.com/books?id=afJdDwAAQBAJ&pg=PA84 |
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| page = 84–89 |
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| publisher = Hindustan Book Agency |
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| isbn = 978-93-86279-06-4 |
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| doi = 10.1007/978-93-86279-06-4 |
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}}</ref> |
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}} |
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==External links== |
==External links== |
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{{Johnson solids navigator}} |
{{Johnson solids navigator}} |
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{{Polyhedron-stub}} |
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Revision as of 01:08, 14 March 2024
| Biaugmented triangular prism | |
|---|---|
 | |
| Type | Johnson J49 – J50 – J51 |
| Faces | 10 triangles 1 square |
| Edges | 17 |
| Vertices | 8 |
| Symmetry group | |
| Properties | convex |
| Net | |
 | |
In geometry, the biaugmented triangular prism is a polyhedron constructed from a triangular prism by attaching two equilateral square pyramids onto two of its square faces. It is an example of Johnson solid.
Construction
The biaugmented triangular prism can be constructed from a triangular prism by attaching two equilateral square pyramids onto its two square faces, a process known as augmentation.[1] These square pyramid covers the square face of the prism, so the resulting polyhedron has 10 equilateral triangles and 1 square as its faces.[2] A convex polyhedron in which all faces are regular is Johnson solid, and the biaugmented triangular prism is among them, enumerated as 50th Johnson solid .[3]
See also
- Augmented triangular prism — the 39th Johnson solid, constructed by attaching a triangular prism with one equilateral square pyramid.
- Triaugmented triangular prism — the 51st Johnson solid, constructed by attaching a triangular prism with three equilateral square pyramids.
References
- ^ Rajwade, A. R. (2001). Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem. Texts and Readings in Mathematics. Hindustan Book Agency. p. 84–89. doi:10.1007/978-93-86279-06-4. ISBN 978-93-86279-06-4.
- ^ Berman, Martin (1971). "Regular-faced convex polyhedra". Journal of the Franklin Institute. 291 (5): 329–352. doi:10.1016/0016-0032(71)90071-8. MR 0290245.
- ^ Francis, Darryl (August 2013). "Johnson solids & their acronyms". Word Ways. 46 (3): 177.