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| {{Prism polyhedra db|Prism polyhedron stat table|P5}}
| | Hi there, I am Sophia. Since I was eighteen I've been working as a bookkeeper but soon my spouse and I will begin our own company. Alaska is the only location I've been residing in but now I'm contemplating other options. Playing badminton is a thing that he is totally addicted to.<br><br>Here is my web page; love psychics ([http://modenpeople.co.kr/modn/qna/292291 My Site]) |
| In [[geometry]], the '''pentagonal prism''' is a [[Prism (geometry)|prism]] with a [[pentagon]]al base. It is a type of [[heptahedron]] with 7 [[Face (geometry)|faces]], 15 [[Edge (geometry)|edges]], and 10 [[vertex (geometry)|vertices]].
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| == As a semiregular (or uniform) polyhedron ==
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| If faces are all regular, the pentagonal prism is a [[semiregular polyhedron]], more generally, a [[uniform polyhedron]], and the third in an infinite set of prisms formed by square sides and two regular polygon caps. It can be seen as a '''[[truncation (geometry)|truncated]] [[hosohedron|pentagonal hosohedron]]''', represented by [[Schläfli symbol]] t{2,5}. Alternately it can be seen as the [[Cartesian product]] of a regular pentagon and a [[line segment]], and represented by the product {5}x{}. The [[dual polyhedron|dual]] of a pentagonal prism is a [[pentagonal bipyramid]].
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| The [[symmetry group]] of a right pentagonal prism is [[dihedral group|''D<sub>5h</sub>'']] of order 20. The [[Point groups in three dimensions#Rotation groups|rotation group]] is ''D<sub>5</sub>'' of order 10.
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| ==Volume==
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| The volume, as for all prisms, is the product of the area of the pentagonal base times the height or distance along any edge perpendicular to the base. For a uniform pentagonal prism with edges ''h'' the formula is
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| :<math>\frac{h^3}{4}\sqrt{5(5 + 2\sqrt{5})}</math>
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| == Use ==
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| Nonuniform pentagonal prisms called [[Pentaprism]]s are also used in optics to rotate an image through a [[right angle]] without changing its [[chirality]].
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| === In polychora ===
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| It exists as cells of four nonprismatic [[uniform polychoron|polychora]] in 4 dimensions:
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| {| class=wikitable width=400
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| |- align=center
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| |[[cantellated 600-cell]]<BR>{{CDD|node|5|node_1|3|node|3|node_1}}
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| |[[cantitruncated 600-cell]]<BR>{{CDD|node|5|node_1|3|node_1|3|node_1}}
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| |[[runcinated 600-cell]]<BR>{{CDD|node_1|5|node|3|node|3|node_1}}
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| |[[runcitruncated 600-cell]]<BR>{{CDD|node_1|5|node|3|node_1|3|node_1}}
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| |- align=center
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| |[[File:600-cell t02 H3.svg|100px]]
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| |[[File:120-cell t123 H3.png|100px]]
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| |[[File:120-cell_t03_H3.png|100px]]
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| |[[File:120-cell_t023_H3.png|100px]]
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| |}
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| == Related polyhedra ==
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| {{UniformPrisms}}
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| ==External links ==
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| * {{mathworld | urlname = PentagonalPrism | title = Pentagonal prism}}
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| *[http://polyhedra.org/poly/show/23/pentagonal_prism Pentagonal Prism Polyhedron Model] -- works in your web browser
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| [[Category:Prismatoid polyhedra]]
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| {{Polyhedron-stub}}
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Hi there, I am Sophia. Since I was eighteen I've been working as a bookkeeper but soon my spouse and I will begin our own company. Alaska is the only location I've been residing in but now I'm contemplating other options. Playing badminton is a thing that he is totally addicted to.
Here is my web page; love psychics (My Site)