Octagonal Prism
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Octagonal Prism
Uniform octagonal prism
Octagonal prism.png
Type Prismatic uniform polyhedron
Elements F = 10, E = 24, V = 16 (? = 2)
Faces by sides 8{4}+2{8}
Schläfli symbol t{2,8} or {8}×{}
Wythoff symbol 2 8 | 2
2 2 4 |
Coxeter diagrams CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 8.pngCDel node.png
CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.png
CDel node 1.pngCDel 2.pngCDel node h.pngCDel 8.pngCDel node h.png
CDel node h.pngCDel 2.pngCDel node h.pngCDel 8.pngCDel node 1.png
Symmetry D8h, [8,2], (*822), order 32
Rotation group D8, [8,2]+, (822), order 16
References U76(f)
Dual Octagonal dipyramid
Properties convex, zonohedron
Octagonal prism vertfig.png
Vertex figure
4.4.8

In geometry, the octagonal prism is the sixth in an infinite set of prisms, formed by square sides and two regular octagon caps.

If faces are all regular, it is a semiregular polyhedron.

Symmetry

Name Ditetragonal prism Ditetragonal trapezoprism
Image Truncated square prism.png Cantic snub octagonal hosohedron.png
Symmetry D4h, [2,4], (*422) D4d, [2+,8], (2*4)
Construction tr{4,2} or t{4}×{}, CDel node 1.pngCDel 2.pngCDel node 1.pngCDel 4.pngCDel node 1.png s2{2,8}, CDel node h.pngCDel 2x.pngCDel node h.pngCDel 8.pngCDel node 1.png

Images

The octagonal prism can also be seen as a tiling on a sphere:

Spherical octagonal prism.png

Use

In optics, octagonal prisms are used to generate flicker-free images in movie projectors.

In uniform honeycombs and 4-polytopes

It is an element of three uniform honeycombs:

It is also an element of two four-dimensional uniform 4-polytopes:

Related polyhedra

External links

  • Weisstein, Eric W. "Octagonal prism". MathWorld.
  • Interactive model of an Octagonal Prism

  This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

Octagonal_prism
 



 



 
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