Octagonal prism

Uniform octagonal prism
File:Octagonal prism.png
Type	Prismatic uniform polyhedron
Elements	F = 10, E = 24, V = 16 (χ = 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	File:CDel node 1.pngFile:CDel 2.pngFile:CDel node 1.pngFile:CDel 8.pngFile:CDel node.png File:CDel node 1.pngFile:CDel 2.pngFile:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.png File:CDel node 1.pngFile:CDel 2.pngFile:CDel node h.pngFile:CDel 8.pngFile:CDel node h.png File:CDel node h.pngFile:CDel 2x.pngFile:CDel node h.pngFile:CDel 8.pngFile:CDel 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
File:Octagonal prism vertfig.png Vertex figure 4.4.8

In geometry, the octagonal prism is a prism comprising eight rectangular sides joining two regular octagon caps.

Symmetry

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

Images

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

File:Spherical octagonal prism.svg

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:

Truncated square prismatic honeycomb File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 4.pngFile:CDel node.pngFile:CDel 2.pngFile:CDel node 1.pngFile:CDel infin.pngFile:CDel node.png	Omnitruncated cubic honeycomb File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.png	Runcitruncated cubic honeycomb File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node 1.png
File:Truncated square prismatic honeycomb.png	File:Omnitruncated cubic honeycomb.jpg	File:Runcitruncated cubic honeycomb.jpg

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

Runcitruncated tesseract File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.png	Omnitruncated tesseract File:CDel node 1.pngFile:CDel 4.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.png
File:4-cube t013.svg	File:4-cube t0123.svg

Related polyhedra

*n42 symmetry mutation of omnitruncated tilings: 4.8.2n
Symmetry *n42 [n,4]	Spherical		Euclidean	Compact hyperbolic				Paracomp.
	*242 [2,4]	*342 [3,4]	*442 [4,4]	*542 [5,4]	*642 [6,4]	*742 [7,4]	*842 [8,4]...	*∞42 [∞,4]
Omnitruncated figure	File:Spherical octagonal prism2.svg 4.8.4	File:Uniform tiling 432-t012.png 4.8.6	File:Uniform tiling 44-t012.svg 4.8.8	File:H2-5-4-omnitruncated.svg 4.8.10	File:H2 tiling 246-7.png 4.8.12	File:H2 tiling 247-7.png 4.8.14	File:H2 tiling 248-7.png 4.8.16	File:H2 tiling 24i-7.png 4.8.∞
Omnitruncated duals	File:Spherical octagonal bipyramid2.png V4.8.4	File:Spherical disdyakis dodecahedron.svg V4.8.6	File:1-uniform 2 dual.svg V4.8.8	File:H2-5-4-kisrhombille.svg V4.8.10	File:Hyperbolic domains 642.png V4.8.12	File:Hyperbolic domains 742.png V4.8.14	File:Hyperbolic domains 842.png V4.8.16	File:H2checkers 24i.png V4.8.∞

External links

• Interactive model of an Octagonal Prism